November 23, 2006
Note: Thanks to John Allen Paulos, online math columnist for ABC News and a specialist on probability theory, for bringing to my attention the prosecutor's fallacy, which now plays a central role in this essay.
Synopsis of essay
Using a "plausibility scale" on a sequence of significant events that occurred on or before Sept. 11, 2001, as recounted in the 9/11 commission narrative, we find that the probability that the commission and official sources of the commission have given a substantially truthful account is less than 0.054.† The rating system gives the government a strong benefit of the doubt in each individual case. Yet, even so, the likelihood that all events are fairly described is minute. This result strongly suggests that the commission and other officials have committed the classical blunder of legal reasoning known as the prosecutor's fallacy (see Appendix H).
In this essay, we seek a way to test the probable accuracy of the official 9/11 commission narrative concerning Sept. 11, 2001. Before getting to the calculation, some preliminaries:
Bayesian probability
Essentially, our method relies on what has come to be called the Bayesian interpretation of probability, which is an alternative to the frequency paradigm. Though the frequency paradigm is generally much to be preferred, there are many cases in which there are insufficient data for frequency methods. But even subjective methods can have their place, with probability numbers used as limiting values.
For more details, please see Cox's theorem at
http://en.wikipedia.org/wiki/Cox%27s_theorem
and Bayesian probability at
http://en.wikipedia.org/wiki/Bayesian_probability
The "expert" assessment assignment of probabilities is echoed in game theoretic economics, whereby the utility is assigned a value so that probabilities may be calculated. So there is ample precedence for the use of subjective probabilities within a scientific framework.‡
Fermi's 'piano tuner' challenge
The physicist Enrico Fermi liked to prod his students to use skimpy data to nevertheless come up with good estimates. A classic example is his challenge to come up with a usable estimate of the number of piano tuners in Chicago.
A NASA math page shows one approach.
https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/fermis_piano_tuner.htm
Here's my method for estimating the number of piano tuners in New York City.
Population is about 7 million. I guess that the average number of residents per household is 3.5 and that there is possibly one piano per 1,000 households. So 7 million/3.5 = 2 million and 2 million/1000 = 2000.
Also, I realize that New York is an entertainment center and on that basis guess that there are possibly 1,000 professionally used pianos.
I conjecture that private pianos are tuned on average of once in five years, whereas professional pianos are tuned on average of twice yearly. So this means about 400 private tunings a year and 2000 public tunings a year for 2400/year total.
Some tuners can do two tunings a day. Others, who have other work, let's say do 3 a week, or 0.5 a day. Taking the average, we get 1.25 tunings/day.
We estimate a tuner works about 240 days a year (50x5 - 5 sick days and 5 holidays). So 240x1.25 = 300 and 2400/300 = 8.
Eight piano tuners intuitively seems low. But I feel relatively safe to say there are fewer than 50 tuners servicing New York City regularly.
A check of Google does not immediately lead to an exact number but does give the qualitative impression that 50 is not far off the mark.
The point here is that, lacking sufficient input data, we did not use standard statistical methods on this problem. But the fact that such statistical ideas as standard deviation, probability distribution and confidence interval were not used does not prevent us from obtaining a qualitative first approximation of the truth. Though it is possible that 50 is way off base, most people who follow the thinking above would accept the number as reasonable.
That said, we must underscore a point made previously on this blog: probability questions can be slippery and answers counterintuitive, as we learn from the prosecutor's fallacy.
The prosecutor's fallacy
The prosecutor's fallacy is based upon a misunderstanding of conditional probability, whereby, in most instances, the probability of A, given B, does not equal the probability of B, given A. Yet there is a tendency to implicitly assume that since p(A, given B) is x, then p(B, given A) must also be x. The probability that a person is innocent, given the evidence, is not the same as the probability that the evidence is sound, given that the assumption of innocence. That is, it is true that in most cases where there is "extensive" evidence, the person is guilty. But this is not the same as the probability that the person is guilty.
A related area of contention stems from the problem of false positives. A test for the presence of an illicit drug in a person's body may be 95% accurate. But this does not imply that the person has a 95% probability of having used the drug. The probability could well be much lower. The test must be used in conjunction with other independent checks.
In the American system, a defendant is not required to prove his innocence. So if the government in effect is saying that "we have a lot of evidence here and in most other cases a lot of evidence brings a guilty verdict," this is fallacious reasoning.
But suppose a defendant unwisely gives the police a list of things he was doing prior to a homicide, hoping the appearance of cooperation will deflect suspicion. The police have a right and a duty to examine the plausibility of the defendant's claims point by point. If all his accounts of events, except for one, are reasonable, his veracity will be seriously impugned.
If his defense attorney tells the jury that the defendant is innocent based on an overwhelming number of true statements, the attorney will be committing the "defense attorney's fallacy," which is simply a variant of the prosecutor's fallacy.
In the matter of the 9/11 commission narrative, what we have done is underscore the severity of the prosecutor's fallacy committed by the commission. We have shown that, despite the wide range of evidence, the official account is highly implausible because it is almost impossible that every claim that includes a string of not-terribly-plausible claims is substantially accurate. Yet, if one claim turns out to be substantially false, the commission's whole theory is thrown into deep doubt.
Demonstration of a cover-up does not necessarily imply an "inside job." Cover-ups tend to benefit not only the guilty, but also those whose job performance would be open to question.
However, in this case, the substance of what is being covered up does tend to imply an "inside job," as will be clear when reading the list of events, plus informed comment, below.
Probabilities for independent events Suppose that we have a series of events each of which tends to occur with a frequency of 90 percent. That is, the event occurs with a probability of 0.9. Now suppose we have 20 events, each of which occurs in 90 percent of cases. Assuming that no event is influenced by a previous event, what is the probability that all 20 events will occur? We simply multiply the probabilities, getting 0.9^20 = 0.122, or a bit over 12%. That is, here there is about an 88% chance that at least one event did not turn out as expected.
Contrast this result with 0.9920, which is equivalent to about 81%. That is, for events that each tend to occur with 99 percent probability, there is a "strong" probability that all 20 independent events will occur.
Now consider an examiner who is testing your probable veracity with a list of 10 questions. On each of nine questions, s/he scores your probable veracity at 95%. But to the question, "Have you ever lied?", you reply, "No." You are very likely to get a score of less than 10 percent for that reply. Again, considering each question as essentially independent of all others, we simply multiply the probabilities, for 0.959x0.10, which is equivalent to 6.3%. The overall probability of a set of independent events is always lower than the lowest probability for one element.
In this case, one examiner might say that you are on average 82% reliable. However, another would conclude that your reliability has to be measured by the lowest score and that your reliability is at the very untrustworthy level.
A very important point here is that one cannot increase the probability for the entire set by adding highly probable events. Inclusion of more events will simply result in a score that is less than or equal (equal if a new event has a 100% probability) to the previous lowest score. The only way to increase the set's probability is to obtain new information that raises a probability of one or more events in the set.
To get a feel for independent events, we ask the question: What is the chance you flip a coin twice and get head, tail (in that order), roll three dice and get 3,2,3 (in that order) and then buy the sole winning raffle ticket out of 1,000 sold.
The chance of all those separate events occurring is 0.000001157, or about as much chance as a snowball in hell. (Note that the chance of a 3,2,3 is identical to the chance of, say, a 2,3,3, but is not identical to the chance of exactly one 2 and two 3's in any order.]
But, we must beware taking a group of independent events that are only randomly related. After all, someone sometime has flipped a coin and obtained HT; and someone sometime has rolled three dice and obtained 3,2,3; and someone sometime has picked a winner from a raffle of 1,000 tickets.
Suppose you are a veteran gambler. We might conjecture that the probability you once flipped a coin and got HT is 0.99, once rolled a die three consecutive times and got 3,2,3 is 0.99 and once chose the sole winning ticket out of 1000 sold as maybe 0.5, for a combined probability of about 49%, which is considerably greater than the odds for a snowball in hell.
So there must be some reason to connect the events in the set. Usually, we are thinking of a single experiment with "short" time intervals between events or composed of simultaneous events. Or, we may be thinking of a narrative of events connected by, for example, a supposed plot, as in the reported al Qaeda plot leading up to 9/11.
Our biggest hurdle is the issue of uniqueness. If an event is truly unique, then there are no frequencies associated with it and hence no means of assessing a real probability of occurrence. However, in human affairs, even an event described as unique is usually a description of a set of routine events that do have learnable frequencies and probabilities.
Perhaps an experienced observer, who has a "feel for" the plausibility of a particular type of event, is, below the level of consciousness, assigning weights to a number of "imponderables." Intuition can be wrong, as any number of victims of false inferences can attest. On the other hand, intuition is often right because of this ability to weight difficult-to-apprehend influences.
In any case, a most important point about the fallacy is burden of proof. Under the American system, a defendant is not required to prove his truthfulness. That is, suppose a defendant unwisely testifies in his defense and gives a series of lame explanations. Even if any one explanation is plausible, the explanations taken together make the probability low that he is being 100 percent truthful. On the other hand, the prosecutor must prove guilt beyond a reasonable doubt. A sequence of probabilities is very often not a proof.
Occam's razor and forensic science
The principle of Occam's razor may be defined as the belief held by most scientists that the most plausible explanation for a set of related events is the one that requires the least number of separate causes.
Consider three homicide scenarios:
Notice that the qualitative probabilities are deliberately set considerably higher than presumed real probabilities. A real probability of 27% in favor of innocence would generally be considered as a reflection of reasonable doubt.
So in that case, if there were four or five such homicide scenarios that each carried a "high" qualitative probability of 0.65, his probability of innocence if all scenarios were considered would be about 18% to 12%, which are higher than the real probabilities. That is, we'd feel comfortable saying the likelihood of his guilt is less than one of these upper bounds. Though a bit crude, this method suffices for a sufficiently large number of related, but independent events.
The principle of Occam's razor says that the probability that there are three separate, or independent, explanations for the husband's actions is far less than the probability of a single explanation: that he is the killer. However, our skeleton description leaves open the possibility that we could still fall into the prosecutor's fallacy.
Of course, behind a typical homicide case are FBI databanks of relevant statistics.
So, we'd be able to introduce the usual paraphernalia of statistical analysis, such as probability distributions, standard deviations, confidence intervals, regression lines and so on. However, why bother? Most of us would find the conclusions above reasonable enough.
Now when we consider an event like the CIA failing to place two terror suspects on a State Department watch list, we are in a difficult area. There are many components that go into such an event and the relevant statistical data are nonexistent or unavailable. However, most scientists agree with the notion that no event can be assessed as 100 percent certain. So a claim based on such an event has a probability of less than 1. If we have almost no reason to suspect a claim, we can assign it a probability of 0.99.
A scale of qualitative, relative probabilities
As we saw in the piano tuner example, qualitative probabilities are not necessarily unscientific.
Here I propose a scale of qualitative, relative probabilities for assessing the confidence that an experienced observer -- in this case a former newspaper reporter accustomed to sizing up official statements -- has in the accuracy of a particular claim. The plausibility scale assumes that any government claim has a minumum probability of accuracy of 70%. That is, claims that are highly implausible still are given a heavy benefit of the doubt in favor of accuracy.
The reader is invited to substitute his own probabilities for the accuracy of the accounts listed below. He might, if he wish, properly "fib" a bit, and grant a probability of 99% to a claim that in his heart he disbelieves but has insufficient cause to question.
Assessing the 9/11 commission's narrative
Some may accuse us of cherry-picking events that tend to point to government deception while bypassing those that help the government's case. But, as noted above, the overall probability of accuracy is always less than the lowest score in the set. So including events of 0.99 probability will not help a low overall score.
Each claim we are contemplating represents an event that, had it turned out differently, would either have resulted in the aborting of what is said to be al Qaeda's mission or would have resulted in a drastically different attack scenario or, if false, very seriously impugns the credibility of government sources.
We are giving a qualitative probability to each commission claim, which is deliberately set substantially above 50% in the commission's favor. Yet, to be able to arrive at some assessment, we employ the relative values listed in the table above.
Also, we must take care to assign each probability as if it is independent of the others. That is, there is a natural tendency to begin lowering probabilities after reading a few incidents because one's sense of doubt begins to increase. But, as we are not using conditional probabilities, we must avoid that temptation.
And, be aware that the order of the incidents is irrelevant to a calculation of the probability of independent events.
Also, there is no requirement to list more events if the set's probability is already low. The probability can only rise if some of the elements are assigned new probabilities based on new information.
What follows is largely, though not exclusively, drawn from the commission report with qualitative probabilities assigned to the claims or implications associated with the event. In the background sections, it should be understood that the scenario is, in most cases, taken from the commission's own assertions. In the first case cited, the commission decided not to publish the incident, but it is relevant to the commission's narrative.
We list 43 events. Had all descriptions been estimated at 0.99 probability of accuracy, 0.9943 is equivalent to about a 65% likelihood of substantive truthfulness, which is a very respectable level of plausibility. However, the cited events cannot measure up to that standard except in three cases. Now suppose we arbitrarily rate all other events at a plausibility measure of 0.95. In that case, we calculate (0.9540)(0.993) = 0.125, or about 12.5% probability that the government is being truthful versus 87.5% probability of a coverup.
However, these ratings are far too generous to the government, as a reading of the events discloses. Collecting the assigned probabilities together yields
(0.993)(0.9510)(0.97)(0.858)(0.83)(0.755)(0.78) =
0.0005303361194787504428381660233787926354219931659698486328125 (according to WolframAlpha). That is, we have 0.053 percent probability that government officials are substantially truthful. Conversely, the probability exceeds 99% that officials are covering up evidence pointing to the real killers.
Now we must be clear that this sort of probability analysis is meant as a means of
On point b, it may be objected that multiplication of numbers associated with independent claims implies frequencies that simply do not exist or, if they do, cannot be ascertained. The reply: just as a ranking system is essentially an analogue of a frequency basis, so the multiplication mimicks what is done for frequencies. As mentioned, there is no claim that the numbers represent anything much beyond degrees of belief.
(This whole matter has been discussed a number of times, including by J.M. Keynes† in his work of philosophy titled A Treatise on Probability [Macmillan 1921]. I cover the issue in my e-book, The Many Worlds of Probability, Reality and Cognition.)
Background: At least a year before 9/11, a top-secret data-mining project had identified Mohamad Atta as a probable member of an al Qaeda cell in the United States. The commission staff did not think the matter worthy of mention. The commission claims that the identification was irrelevant and Pentagon officials have said the project was killed because of legal concerns.
Claims or implications: The identification of Atta ahead of time does not indicate that intelligence officials had advance knowledge of the 9/11 attacks.
We assign a probability of accuracy of 0.9 (or 90%), remembering that we are making our estimates high in favor of the government.
Background: In Sept 1998, CIA chief George Tenet told lawmakers that the CIA knew more about the Bin Laden network than about any other top-tier terror network. The CIA had been highly successful in disrupting al Qaeda's Albania-based terror cells, having captured a number of al Qaeda operatives who were then detained by governments friendly to the CIA. Seized by German police was Abu Hajer, al Qaeda's chief of computer operations and weapons procurement.
Claims or implications:
A. The CIA was unable to turn any of these Qaeda agents for use as CIA double agents, or, even if they did, gained no useful inside information concerning 9/11 preparations.
Probability of accuracy: 0.9
B. The CIA did not obtain enough information from Hajer to penetrate al Qaeda's electronic communications, or al Qaeda took strong electronic security precautions once Hajer was captured.
Probability of accuracy: 0.9
C. The CIA did not control the 9/11 operation through the use of double agents.
Probability of accuracy: 0.9
Background: In late 1999, four jihad volunteers from Germany were selected by Bin Laden as "core members" of the 9/11 plot with "remarkable speed," with no comprehensive training or testing of their military preparedness in al Qaeda training camps or on actual terror operations. Atta was quickly given responsibility for the operation, probably based on his personal character, technical ability and familiarity with western ways.
Claims or implications: Atta and the other three were given a big part in such a complex undertaking almost off-handedly.
Probability of accuracy: 0.85
Background: On Sept. 28, 2000, Israel's Ariel Sharon sparked wide outrage among many Muslims for a much-publicized tour of a disputed Jerusalem religious site. The tour touched off rioting and an intifada among Palestinians and was quickly a source of bitter resentment in the Arab world.
Claims or implications: The U.S. government, though generally aware of a potential big strike by bin Laden on U.S. interests, was not specifically concerned about the month of September as a likely time of reprisal, or, if so, thought the attack would be against Israeli interests.
Probability of accuracy: 0.95
Background: In the late 1990s, the CIA considered means of capturing Bin Laden at his compound near the Kandahar airport. The agency was repeatedly frustrated despite several seemingly plausible opportunities. One argument was that mountain tribesmen, while providing good intelligence on Bin Laden, would not conduct a raid on behalf of the CIA.
Claims or implications: The CIA did not deliberately refrain from nabbing Bin Laden as part of a larger scheme to use al Qaeda as a useful pawn.
Probability of accuracy: 0.95
Background: Several plans to knock out Bin Laden with a cruise missile were rejected.
Claims or implications: The possibility of high civilian casualties was too great for the Clinton White House to accept.
Probability of accuracy: 0.99
Background: The "get bin-Laden unit" in the White House and CIA always rejected the idea of a commando raid by U.S. forces.
Claims or implications: A big concern was the possibility such a raid might fail, as did a failed attempt to rescue U.S. hostages in Iran during President Carter's tenure.
Probability of accuracy: 0.99
Background: A top al Qaeda operative and 9/11 mastermind was Khalid Sheikh Mohammed, who in the 1980s obtained a degree in mechanical engineering from a college in the United States and then joined the anti-soviet jihad in Afghanistan. The CIA was a major bankroller of the mujahideen fighters.
Claims or implications: KSM had no contacts with the CIA during the Russian-Afghan war, or, if so, they were minor and the CIA had no dealings with him later.
Probability of accuracy: 0.95
Background: In March 2000, Atta emailed 31 different U.S. flight schools on behalf of a small group of men from Arab countries who were studying in Germany.
Claims or implications: This email was not brought to the attention of U.S. security authorities, or, if so, the intelligence was lost in the bureaucracy.
Probability of accuracy: 0.95
Background: The attacks of 9/11 were reputedly an evolution of al Qaeda plans to bomb 10 airliners over the Pacific or to use hijacked planes as missiles before or during 2000. The CIA had some knowledge of these plans from Phillipines authorities who had captured KSM's nephew after he bombed a Philippines airliner and a movie theater. The nephew had also been a principle in the 1993 bombing of the World Trade Center.
Claims or implications: The CIA and FBI were failing to "connect the dots."
Probability of accuracy: 0.9
Background: Though al Qaeda had reputedly been responsible for two bombings of U.S. embassies and was known for an eagerness to inflict high casualties, and had reputedly mulled over the idea of coordinated attacks on U.S. jetliners, the terrorists had never yet carried out such a complex, wide-ranging precision operation.
Claims or implications:
A. Al Qaeda went ahead with the operation despite the risks of failure.
Probability of accuracy: 0.9
B. Al Qaeda was unconcerned, perhaps because of religious zealotry, about overplaying its hand and instigating a war against its Taliban hosts.
Probability of accuracy: 0.95
Background: A National Security Agency electronics intercept led the CIA to observe 9/11 hijackers Khalid al Mihdhar and Nawaf al Hazmi at a meeting of terrorists in Kuala Lumpur in January 2000. The agency knew Mihdhar was a terrorist and knew enough to get more information on Hazmi. The pair was tracked by the CIA but reportedly lost on the teeming streets of Bangkok. The CIA's counterterror center told no one outside the unit of the cold trail, the CIA did not register either on the State Department's terror suspect watchlist and the FBI was kept in the dark. As a result, the pair was able to enter and leave the United States several times with no notice. These events occurred at a time when U.S. security services were worried about a major "millenium" terrorist attack in the United States or against U.S. interests.
Claims or implications: Bureaucratic problems and interagency rivalry let slip an opportunity to keep track of people who were likely leads in a "millenium plot" against the United States.
Probability of accuracy: 0.85
Background: Al Qaeda commander Khalid Sheikh Mohammed reportedly told CIA interrogators that he broke the usual security protocols and urged Mihdhar and Hazmi, who were unfamiliar with western culture, to seek help at a southern California mosque upon entry into the United States. The other hijackers, however, were given explicit instructions to melt into the culture and steer clear of mosques and radical Islamic associates.
Claims or implications: Al Qaeda was not only dealing with Arabs, who have a reputation as a rough-hewn lot, but with men who had pledged to martyr themselves. Hence, it was difficult to control them as one might control professional intelligence agents. On the other hand, Atta's "Hamburg group" seemed to take orders relatively well.
Probability of accuracy: 0.75
Background: Mihdhar, while trying to obtain flight training for his suicide mission, became bored with life in America and flew back to Yemen to visit his newborn son. KSM reputedly told CIA interrogators that he then tried to drop Mihdhar from the operation, but Bin Laden overruled him.
Claims or implications: Because of personal qualities or internal al Qaeda politics, Bin Laden carelessly jeopardized an extremely important operation.
Probability of accuracy: 0.75
Background: The housemate who rented a room to Mihdhar and Hazmi had longstanding contacts with the FBI and local police. He reported nothing to authorities about the pair.
Claims or implications: The hijackers were not placed in a "safe house" by federal operatives.
Probability of accuracy: 0.95
Background: Hijacker Jarrah took five overseas trips from the United States, including one to visit his girlfriend in Germany. Various other hijackers went on holiday overseas during 2001.
Claims or implications: Al Qaeda was unworried about exposing operatives to so many opportunities to attract surveillance, or leaders felt they couldn't force a probable martyr to observe security precautions.
Probability of accuracy: 0.75
Background: Zacarias Moussaoui, a supposed back-up hijacker, sent inquiries to Airman Flight School in Oklahoma from London, where he stayed at a dormitory for Islamic men. British security authorities were conducting intensive counterterrorism investigations and operations, the commission has said.
Claims or implications: Moussaoui's inquiry either did not attract the attention of MI5, or, if so, the matter was filed away with no action taken; but if MI5 notified U.S. authorities, the matter was lost in the bureaucracy.
Probability of accuracy: 0.95
Background: Hijacker Hanjour, while living in Arizona in the 1990s, associated with several people who had been subjects of terrorism investigations. Some trained with Hanjour to be pilots. Others had connections to al Qaeda and Afghan training camps. A number of Arab "freedom fighters" with CIA connections lived in the region at that time.
Claims or implications:
A. On returning to America, Hanjour was not "helped" by past association with the CIA and, at any rate, bureaucratic issues spared him surveillance of a type that would have led to exposure of the plot.
Probability of accuracy: 0.85
B. Additionally, his past associations did not cause him to be placed on a State Department watchlist for terror suspects.
Probability of accuracy: 0.7
Background: During an al Qaeda meeting in Spain, Atta mentioned a jetliner attack on a nuclear plant near New York City. The idea was rejected because the airspace around the plant was restricted and the attack plane might get shot down. Other reasons for rejecting the idea: the plant didn't have symbolic value; top al Qaeda leaders hadn't been consulted.
Claims or implications: The plotters were worried about a shootdown near a nuclear plant but not near the Pentagon, White House or Capitol.
Probability of accuracy: 0.75
Background: President Bush was away from the capital at the time of the attack. If we estimate that he normally spends about 50 days outside the capital, the probability he would be absent on Sept. 11 is 50/365, which is equivalent to about 14%.
Claims or implications: Bush's absence does not indicate advance knowledge of the attacks either on his part or on the part of top aides.
Probability of accuracy: 0.99
Background: In 2001, there were numerous warnings of a major terrorist strike in the offing against the United States reaching federal security officials. Warnings include a June 12 CIA report noting that Khalid Sheikh Mohammed was recruiting people to travel to the United States for an al Qaeda strike (a "spectacular" high-casualty attack was forecast for the end of June); on June 25, six separate intelligence reports told of an impending al Qaeda attack; multiple calamitous attacks were expected; on Aug. 6, a presidential daily brief says the FBI was busy with 70 Bin Laden-related terror investigations, the bureau having detected suspicious activity, such as surveillance of federal buildings in Manhattan, inside U.S. borders consistent with preparations for plane hijackings or other types of attacks.
Claims or implications:
A. No one with real power at the National Security Council level knew enough to "get it together" and make sure airport security was beefed up, but simply relied on alerts to the Federal Aviation Agency that were treated in a bureaucratic fashion.
Probability of accuracy: 0.85
B. The FBI had insufficient data to pinpoint Atta and the others, or if so, the intelligence was lost in a bureaucratic maze.
Probability of accuracy: 0.85
Background: In January 2001, a CIA officer established links between Mihdhar and a terrorist involved in the bombing of the USS Cole. But, at this juncture, the agency appears to have made no effort to find Mihdhar and his Kuala Lumpur companion.
Claims or implications: Some CIA unit was not "running" Mihdhar as an agent.
Probability of accuracy: 0.95
Background: The commission disputes the recollections of CIA chief Tenet and CIA counterterror officer Cofer Black that the FBI had access to the identification of Mihdhar as of January 2001. Reportedly, the FBI did not know that Mihdhar had a U.S. visa, and so made no attempt to find him.
Claims or implications: Bureaucratic problems and interagency rivalry prevented the FBI from hunting down a person with strong terrorist ties. The FBI was not acquiescing in a CIA decision to protect one of its assets. [Mihdhar could have had CIA friends at this point without being an active asset.]
Probability of accuracy: 0.85
Background: In mid-May 2001, a CIA officer detailed to an FBI counterterror unit puzzled over where al Qaeda was likely to strike. A database search of those spotted in Kuala Lumpur disclosed Mihdhar's international travels. The database disclosed that Mihdhar had landed at Los Angeles on Jan. 15. For bureaucratic reasons, Mihdhar was not put on a State Dept. terror watchlist -- despite his known terrorist associations -- and so his travels to and from the United States after May went undetected. Had the FBI put him under watch, the entire 9/11 plot is likely to have unraveled.
Claims or implications: The failure to put Mihdhar on a watchlist had nothing to do with his probable past associations with CIA-backed Arab jihadists in Arizona.
Probability of accuracy: 0.8
Background: In June 2001, an FBI analyst posted to the CIA's Bin Laden unit met with FBI agents probing the Cole case in order to pump them for information. She showed surveillance photos, which included imagery of Mihdhar, to her fellow agents but then rebuffed their attempts to learn more about the people in the photos. FBI counterterror agents would probably have tracked Mihdhar to southern California, quite possibly foiling the 9/11 plot, had the analyst not, in a mistaken interpretation of national security rules, refused them the background data. Hence, Mihdhar received a new U.S. visa two days after this meeting.
Claims or interpretations: The analyst did not withhold data that would likely have prevented the 9/11 attacks because of human fallibility and not because she was aware of at least some aspect of a deep-laid plot.
Probability of accuracy: 0.95
Background: In August 2001, a CIA officer with the Bin Laden unit asked an FBI analyst to review all Kuala Lumpur materials one more time. The two women discovered Mihdhar's U.S. entry and exit records and noted that Hazmi had accompanied Mihdhar to Los Angeles in January 2001. They wanted Mihdhar found, thinking Hazmi was no longer in the United States. Both Mihdhar and Hazmi were placed on the terrorist watchlist. However, the FBI analyst lacked agency status and so conveyed a "routine" priority to the FBI's Manhattan field office, which was handling the Cole case, to find Mihdhar. A routine request would get little immediate attention, meaning the Manhattan field office was barely aware of Mihdhar before the 9/11 attacks.
Claims or implications: An FBI employee posted to a top-priority counterterror unit lacked sufficient status to trigger a major manhunt; the fact that such a terrorist was known to authorities at the highest levels of national security does not indicate prior knowledge of the 9/11 attacks.
Probability of accuracy: 0.9
Background: An FBI agent with the Phoenix field office in July 2001 sent a memo to FBI headquarters and to New York field office terrorism agents warning of the likelihood that Bin Laden was sending students to civil aviation schools in America. The agent noted an "inordinate number of individuals of investigative interest" attending such schools in Arizona. He urged a thorough program to check flight schools.
Claims or implications: The warning, which preceded a warning from the Minneapolis field office concerning suspicious flight school activity, fell on deaf bureaucratic ears -- despite the intensive interest of the Cole case squad in New York in Bin Laden's activities and the fact that Washington intelligence units were highly aware that an attack was imminent.
Probability of accuracy: 0.7
Background: On Aug. 15, 2001, the FBI's Minneapolis office initiated an intelligence investigation of Zacarias Moussaoui after his flight school instructor became suspicious of the aggressive, erratic Arab, who seemed uninterested in learning how to fly properly. Moussaoui was unabashed at revealing his jihadist beliefs to an FBI agent and the field office became convinced that he was planning a hijacking, though the bureau did not at that time learn that he had received money from an al Qaeda operative. The field office tried to interest headquarters in the Moussaoui case but the response was desultory. The field office also got caught up in a bureaucratic wrangle that prevented agents from examining Moussaoui's laptop computer, which, as it turned out, contained important evidence. The CIA contacted London about Moussaoui, identifying him as a "possible suicide hijacker" but London was overwhelmed with terrorism inquiries and gave the matter little attention. Still, the Minneapolis field office sent out a general warning, sharply edited at headquarters insistence, to the FAA, followed up by agents giving in-person, detailed oral warnings to FAA officials, but the FAA response was minimal.
Claims or implications: Though Moussaoui was not viewed as a person of significant interest at headquarters, this fact does not indicate that he was a "known quantity," perhaps a pawn in an intelligence game. Also, this "suicide hijacker" alert did not raise alarm bells concerning the Phoenix memo.
Probability of accuracy: 0.75
Background: The FBI's Minneapolis field office wanted to prevent a hijacking and so arranged for the Immigration and Naturalization Service to hold Moussaoui on an immigration violation in preparation for deportation. Neither Bin Laden nor Khalid Sheikh Mohammed, who was running the 9/11 operation, was aware that Moussaoui had disappeared, but even so, al Qaeda spontaneously sent a more reliable suicide pilot to take his place.
Claims or implications: Al Qaeda was so disorganized that it didn't notice that one of its "glory mission" pilots had vanished but so organized that it kept the highly complex plot moving. Moussaoui's flight training was not arranged in advance to provide "evidence" of al Qaeda's responsibility.
Probability of accuracy: 0.7
Background: Two days before Sept. 11, operational chief Atta and another hijacker went to Portland, Me., for no known reason. Then on the fateful day, at 5:58 a.m., the two men flew from the Portland jetport to Boston's Logan International Airport, where they were to hijack American Airlines Flight 11. As it happens, the flight from Portland was late arriving and caused Atta's baggage to be left at Logan, rather than being trasnferred onto AA11.
After the fiery events, the FBI searched baggage at Logan and found Atta's luggage, which contained various items that pointed to al Qaeda, according to contemporary press accounts. In 2004, after the 9/11 commission report was released, an ex-Boston FBI agent told the Boston Globe that the commission had kept silent on the contents of Atta's luggage, which included all the names of the hijackers and other material underscoring the plot. The agent described the contents as the "Rosetta stone" pointing to al Qaeda. His account was verified by a former federal prosecutor, the Globe said.
In October 2001, investigative reporter Seymour M. Hersh is quoted to have written that he had been told by an intelligence official that the contents of Atta's bags had been planted for authorities to find. Even so, the FBI has stuck with this account. The commission's decision to suppress the details of Atta's baggage seems to be a reflection of the credibility of the story. [A copy of Hersh's story was unobtainable via Google or the New Yorker's search engine.]
Claims or implications:
A: Atta was unworried that the entire mission, which relied on near closely timed hijackings, would have been derailed had he and his associate missed their connection at Logan.
Probability of accuracy: 0.7
B: The evidence found in Atta's luggage was not planted there in order to provide a quick accusation against al Qaeda.
Probability of accuracy: 0.7
Background: Atta chose Logan, which is hundreds of miles from New York, to launch strikes against the Trade Center, rather than Newark airport, which is only a few miles from Manhattan. However, Newark was the launchpad for the hijacking of United Airlines Flight 93, which crashed in Pennsylvania. It is possible that two fuel-heavy Los Angeles-bound jets weren't available at Newark and Atta wanted to keep the trade center flights relatively close in time.
Claims or implications: There is nothing especially peculiar about the decision.
Probability of accuracy: 0.95
Background: At Washington's Dulles airport, three hijackers were flagged by a computer program used to profile terror suspects. Two were quizzed because of suspicious behavior, including the fact that one hijacker failed to produce a photo ID.
Claims or implications: Al Qaeda -- in particular operations chief Atta -- was recklessly casual and would overlook ensuring that every hijacker had a photo ID.
Probability of accuracy: 0.7
Background: Altogether, nine of 19 hijackers were identified by airport screenings as security risks. Atta was profiled in Portland; three were profiled at Dulles; and at Logan the others were profiled. But, not expecting suicidal persons, airline security protocols called only for holding a suspect's baggage off the plane until after he had boarded. So all the hijackers were waved through security checkpoints.
Claims or implications: The hijackers were not given the "high sign" by airport security officials controlled by the CIA or other intelligence unit.
Probability of accuracy: 0.85
Background: AA11 dove from about 26,000 feet, making a sharp turnabout and rammed WTC 1 at nearly 500 mph. UA175 made a similar maneuver, banking sharply just before striking WTC2 at some 600 mph. The pilots had never flown jumbo jets and were barely competent in the cockpit, though they had had training on jumbo jet simulators and could fly smaller aircraft. For example, AA11 hijackers supposedly accidently broadcast to other planes an intercom warning to passengers to remain calm. Even so, the pilots showed remarkable prowess at handling the planes and making sure they hit their targets at these high speeds.
Claims or implications: The al Qaeda pilots had learned enough to qualify for this one "stunt" and the planes, whether hijackers were aboard or not, were not operated by Predator-style remote controls from on the ground.
Probability of accuracy: 0.8
Background: Al Qaeda's AA77 pilot, despite poor grades in flight school, performed a stunt with the jumbo jet worthy of the best Air Force fighter pilots. Upon returning the plane to D.C., he dove from 7000 feet to 2200 feet at which height he executed a 330-degree turn (a very sharp loop), aiming the plane for the Pentagon. He gunned the plane to maximum acceleration and then plowed into the Pentagon. This is a difficult maneuver for a fighter jet, let alone a jumbo jetliner. The risk of failing to pull out of such a dive was rather large.
The success of this stunt reportedly prompted President Bush, an experienced pilot, to wonder aloud about the hijacker's ability.
Claims or implications: The Pentagon was not struck by a bomb; or the Pentagon was not struck by a cruise missile; or the Pentagon was not struck by a remotely controlled aircraft, whether fighter plane or AA11.
Probability of accuracy: 0.7
Background: WTC2 collapses less than an hour after UAW175's strike. Nearly everyone below the crash site had cleared the building because they used elevators. WTC1 collapses an hour and a half after being struck by AA11, with thousands still trapped inside. Hours later, another building in the complex, the 47-floor WTC7 collapses. The National Institutes for Standards and Technology admittedly had a difficult time finding computer simulations leading to the collapse of each of the twin towers. The buildings had been designed to withstand jetliner impacts and no major structural steel building anywhere is known to have collapsed due to fire prior to 9/11. The collapse of WTC7 was assigned a "low probability" by investigators for the Federal Emergency Management Agency.
Claims or implications:
A. Neither of the twin towers was brought down by controlled demolition.
Probability of accuracy: 0.85
B. WTC7 was not brought down by controlled demolition.
Probability of accuracy: 0.7
Remotely controlled 9/11 planes?
The government's own research into the collapses of the trade center towers strongly suggests the use of explosives -- despite what the final report claims. Now would plotters have gone to all the trouble to rig the twin towers with explosives unless they were very, very sure that each would be struck by a plane?
Counting on some ill-trained jihadists would be a fairly iffy proposition. Suppose the hijack went awry, or the hijack pilot got cold feet, or got lost, or missed his assigned tower because of the difficulty of the maneuver...
Hence, this leads us to strongly suspect that, whether hijackers were really aboard or not, the planes were handled by remote control from the ground, using Predator-style technology. This seems even more likely considering the amazing high-G maneuver of the plane that (presumably) struck the Pentagon.
Though Americans knew about cruise guided missiles, they hadn't heard of the Pentagon's secret Predator technology until well after 9/11.
† Tending to bolster our desire for a "plausibility scale," we read that J.M. Keynes in his A Treatise On Probability (Macmillan 1921) preferred the concept of propositional truth to that of supposed "events."
‡ A case for subjective, though informed, opinion in probability assessment is made by The Subjectivity of Scientists and the Bayesian Approach by S. James Press and Judith M. Tanur (John Wiley 2001).
Note: Thanks to John Allen Paulos, online math columnist for ABC News and a specialist on probability theory, for bringing to my attention the prosecutor's fallacy, which now plays a central role in this essay.
Synopsis of essay
Using a "plausibility scale" on a sequence of significant events that occurred on or before Sept. 11, 2001, as recounted in the 9/11 commission narrative, we find that the probability that the commission and official sources of the commission have given a substantially truthful account is less than 0.054.† The rating system gives the government a strong benefit of the doubt in each individual case. Yet, even so, the likelihood that all events are fairly described is minute. This result strongly suggests that the commission and other officials have committed the classical blunder of legal reasoning known as the prosecutor's fallacy (see Appendix H).
In this essay, we seek a way to test the probable accuracy of the official 9/11 commission narrative concerning Sept. 11, 2001. Before getting to the calculation, some preliminaries:
Bayesian probability
Essentially, our method relies on what has come to be called the Bayesian interpretation of probability, which is an alternative to the frequency paradigm. Though the frequency paradigm is generally much to be preferred, there are many cases in which there are insufficient data for frequency methods. But even subjective methods can have their place, with probability numbers used as limiting values.
For more details, please see Cox's theorem at
http://en.wikipedia.org/wiki/Cox%27s_theorem
and Bayesian probability at
http://en.wikipedia.org/wiki/Bayesian_probability
The "expert" assessment assignment of probabilities is echoed in game theoretic economics, whereby the utility is assigned a value so that probabilities may be calculated. So there is ample precedence for the use of subjective probabilities within a scientific framework.‡
Fermi's 'piano tuner' challenge
The physicist Enrico Fermi liked to prod his students to use skimpy data to nevertheless come up with good estimates. A classic example is his challenge to come up with a usable estimate of the number of piano tuners in Chicago.
A NASA math page shows one approach.
https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/fermis_piano_tuner.htm
Here's my method for estimating the number of piano tuners in New York City.
Population is about 7 million. I guess that the average number of residents per household is 3.5 and that there is possibly one piano per 1,000 households. So 7 million/3.5 = 2 million and 2 million/1000 = 2000.
Also, I realize that New York is an entertainment center and on that basis guess that there are possibly 1,000 professionally used pianos.
I conjecture that private pianos are tuned on average of once in five years, whereas professional pianos are tuned on average of twice yearly. So this means about 400 private tunings a year and 2000 public tunings a year for 2400/year total.
Some tuners can do two tunings a day. Others, who have other work, let's say do 3 a week, or 0.5 a day. Taking the average, we get 1.25 tunings/day.
We estimate a tuner works about 240 days a year (50x5 - 5 sick days and 5 holidays). So 240x1.25 = 300 and 2400/300 = 8.
Eight piano tuners intuitively seems low. But I feel relatively safe to say there are fewer than 50 tuners servicing New York City regularly.
A check of Google does not immediately lead to an exact number but does give the qualitative impression that 50 is not far off the mark.
The point here is that, lacking sufficient input data, we did not use standard statistical methods on this problem. But the fact that such statistical ideas as standard deviation, probability distribution and confidence interval were not used does not prevent us from obtaining a qualitative first approximation of the truth. Though it is possible that 50 is way off base, most people who follow the thinking above would accept the number as reasonable.
That said, we must underscore a point made previously on this blog: probability questions can be slippery and answers counterintuitive, as we learn from the prosecutor's fallacy.
The prosecutor's fallacy
The prosecutor's fallacy is based upon a misunderstanding of conditional probability, whereby, in most instances, the probability of A, given B, does not equal the probability of B, given A. Yet there is a tendency to implicitly assume that since p(A, given B) is x, then p(B, given A) must also be x. The probability that a person is innocent, given the evidence, is not the same as the probability that the evidence is sound, given that the assumption of innocence. That is, it is true that in most cases where there is "extensive" evidence, the person is guilty. But this is not the same as the probability that the person is guilty.
A related area of contention stems from the problem of false positives. A test for the presence of an illicit drug in a person's body may be 95% accurate. But this does not imply that the person has a 95% probability of having used the drug. The probability could well be much lower. The test must be used in conjunction with other independent checks.
In the American system, a defendant is not required to prove his innocence. So if the government in effect is saying that "we have a lot of evidence here and in most other cases a lot of evidence brings a guilty verdict," this is fallacious reasoning.
But suppose a defendant unwisely gives the police a list of things he was doing prior to a homicide, hoping the appearance of cooperation will deflect suspicion. The police have a right and a duty to examine the plausibility of the defendant's claims point by point. If all his accounts of events, except for one, are reasonable, his veracity will be seriously impugned.
If his defense attorney tells the jury that the defendant is innocent based on an overwhelming number of true statements, the attorney will be committing the "defense attorney's fallacy," which is simply a variant of the prosecutor's fallacy.
In the matter of the 9/11 commission narrative, what we have done is underscore the severity of the prosecutor's fallacy committed by the commission. We have shown that, despite the wide range of evidence, the official account is highly implausible because it is almost impossible that every claim that includes a string of not-terribly-plausible claims is substantially accurate. Yet, if one claim turns out to be substantially false, the commission's whole theory is thrown into deep doubt.
Demonstration of a cover-up does not necessarily imply an "inside job." Cover-ups tend to benefit not only the guilty, but also those whose job performance would be open to question.
However, in this case, the substance of what is being covered up does tend to imply an "inside job," as will be clear when reading the list of events, plus informed comment, below.
Probabilities for independent events Suppose that we have a series of events each of which tends to occur with a frequency of 90 percent. That is, the event occurs with a probability of 0.9. Now suppose we have 20 events, each of which occurs in 90 percent of cases. Assuming that no event is influenced by a previous event, what is the probability that all 20 events will occur? We simply multiply the probabilities, getting 0.9^20 = 0.122, or a bit over 12%. That is, here there is about an 88% chance that at least one event did not turn out as expected.
Contrast this result with 0.9920, which is equivalent to about 81%. That is, for events that each tend to occur with 99 percent probability, there is a "strong" probability that all 20 independent events will occur.
Now consider an examiner who is testing your probable veracity with a list of 10 questions. On each of nine questions, s/he scores your probable veracity at 95%. But to the question, "Have you ever lied?", you reply, "No." You are very likely to get a score of less than 10 percent for that reply. Again, considering each question as essentially independent of all others, we simply multiply the probabilities, for 0.959x0.10, which is equivalent to 6.3%. The overall probability of a set of independent events is always lower than the lowest probability for one element.
In this case, one examiner might say that you are on average 82% reliable. However, another would conclude that your reliability has to be measured by the lowest score and that your reliability is at the very untrustworthy level.
A very important point here is that one cannot increase the probability for the entire set by adding highly probable events. Inclusion of more events will simply result in a score that is less than or equal (equal if a new event has a 100% probability) to the previous lowest score. The only way to increase the set's probability is to obtain new information that raises a probability of one or more events in the set.
To get a feel for independent events, we ask the question: What is the chance you flip a coin twice and get head, tail (in that order), roll three dice and get 3,2,3 (in that order) and then buy the sole winning raffle ticket out of 1,000 sold.
The chance of all those separate events occurring is 0.000001157, or about as much chance as a snowball in hell. (Note that the chance of a 3,2,3 is identical to the chance of, say, a 2,3,3, but is not identical to the chance of exactly one 2 and two 3's in any order.]
But, we must beware taking a group of independent events that are only randomly related. After all, someone sometime has flipped a coin and obtained HT; and someone sometime has rolled three dice and obtained 3,2,3; and someone sometime has picked a winner from a raffle of 1,000 tickets.
Suppose you are a veteran gambler. We might conjecture that the probability you once flipped a coin and got HT is 0.99, once rolled a die three consecutive times and got 3,2,3 is 0.99 and once chose the sole winning ticket out of 1000 sold as maybe 0.5, for a combined probability of about 49%, which is considerably greater than the odds for a snowball in hell.
So there must be some reason to connect the events in the set. Usually, we are thinking of a single experiment with "short" time intervals between events or composed of simultaneous events. Or, we may be thinking of a narrative of events connected by, for example, a supposed plot, as in the reported al Qaeda plot leading up to 9/11.
Our biggest hurdle is the issue of uniqueness. If an event is truly unique, then there are no frequencies associated with it and hence no means of assessing a real probability of occurrence. However, in human affairs, even an event described as unique is usually a description of a set of routine events that do have learnable frequencies and probabilities.
Perhaps an experienced observer, who has a "feel for" the plausibility of a particular type of event, is, below the level of consciousness, assigning weights to a number of "imponderables." Intuition can be wrong, as any number of victims of false inferences can attest. On the other hand, intuition is often right because of this ability to weight difficult-to-apprehend influences.
In any case, a most important point about the fallacy is burden of proof. Under the American system, a defendant is not required to prove his truthfulness. That is, suppose a defendant unwisely testifies in his defense and gives a series of lame explanations. Even if any one explanation is plausible, the explanations taken together make the probability low that he is being 100 percent truthful. On the other hand, the prosecutor must prove guilt beyond a reasonable doubt. A sequence of probabilities is very often not a proof.
Occam's razor and forensic science
The principle of Occam's razor may be defined as the belief held by most scientists that the most plausible explanation for a set of related events is the one that requires the least number of separate causes.
Consider three homicide scenarios:
- A woman is found slain and the husband held for questioning. Witnesses have reported the two had been feuding but other evidence is inconclusive. Suppose we put the probability of his truthfulness as 65%.
- A husband calls police saying his gun discharged while he was cleaning it and his wife is dead. Other evidence is inconclusive. Probability of truthfulness is set at 65%.
- A woman is found slain and her husband is discovered to have recently obtained a passport visa to a country with no extradition treaty with the United States. An avid sportsman, he says he was planning a sporting adventure. Other evidence is inconclusive. Probability of truthfulness is set at 65%.
Notice that the qualitative probabilities are deliberately set considerably higher than presumed real probabilities. A real probability of 27% in favor of innocence would generally be considered as a reflection of reasonable doubt.
So in that case, if there were four or five such homicide scenarios that each carried a "high" qualitative probability of 0.65, his probability of innocence if all scenarios were considered would be about 18% to 12%, which are higher than the real probabilities. That is, we'd feel comfortable saying the likelihood of his guilt is less than one of these upper bounds. Though a bit crude, this method suffices for a sufficiently large number of related, but independent events.
The principle of Occam's razor says that the probability that there are three separate, or independent, explanations for the husband's actions is far less than the probability of a single explanation: that he is the killer. However, our skeleton description leaves open the possibility that we could still fall into the prosecutor's fallacy.
Of course, behind a typical homicide case are FBI databanks of relevant statistics.
So, we'd be able to introduce the usual paraphernalia of statistical analysis, such as probability distributions, standard deviations, confidence intervals, regression lines and so on. However, why bother? Most of us would find the conclusions above reasonable enough.
Now when we consider an event like the CIA failing to place two terror suspects on a State Department watch list, we are in a difficult area. There are many components that go into such an event and the relevant statistical data are nonexistent or unavailable. However, most scientists agree with the notion that no event can be assessed as 100 percent certain. So a claim based on such an event has a probability of less than 1. If we have almost no reason to suspect a claim, we can assign it a probability of 0.99.
A scale of qualitative, relative probabilities
As we saw in the piano tuner example, qualitative probabilities are not necessarily unscientific.
Here I propose a scale of qualitative, relative probabilities for assessing the confidence that an experienced observer -- in this case a former newspaper reporter accustomed to sizing up official statements -- has in the accuracy of a particular claim. The plausibility scale assumes that any government claim has a minumum probability of accuracy of 70%. That is, claims that are highly implausible still are given a heavy benefit of the doubt in favor of accuracy.
70%: Very serious concern as to a claim's plausibility.In the last two cases, we could change the probability to 100% (i.e., ignore those events). This would have little effect on the outcome of the calculation.
80%: Serious concern as to a claim's plausibility.
85%: Concern as to a claim's plausibility.
90%: Mild concern as to a claim's plausibility.
95%: Very mild concern as to a claim's plausibility.
99%: No concern as to a claim's plausibility.
The reader is invited to substitute his own probabilities for the accuracy of the accounts listed below. He might, if he wish, properly "fib" a bit, and grant a probability of 99% to a claim that in his heart he disbelieves but has insufficient cause to question.
Assessing the 9/11 commission's narrative
Some may accuse us of cherry-picking events that tend to point to government deception while bypassing those that help the government's case. But, as noted above, the overall probability of accuracy is always less than the lowest score in the set. So including events of 0.99 probability will not help a low overall score.
Each claim we are contemplating represents an event that, had it turned out differently, would either have resulted in the aborting of what is said to be al Qaeda's mission or would have resulted in a drastically different attack scenario or, if false, very seriously impugns the credibility of government sources.
We are giving a qualitative probability to each commission claim, which is deliberately set substantially above 50% in the commission's favor. Yet, to be able to arrive at some assessment, we employ the relative values listed in the table above.
Also, we must take care to assign each probability as if it is independent of the others. That is, there is a natural tendency to begin lowering probabilities after reading a few incidents because one's sense of doubt begins to increase. But, as we are not using conditional probabilities, we must avoid that temptation.
And, be aware that the order of the incidents is irrelevant to a calculation of the probability of independent events.
Also, there is no requirement to list more events if the set's probability is already low. The probability can only rise if some of the elements are assigned new probabilities based on new information.
What follows is largely, though not exclusively, drawn from the commission report with qualitative probabilities assigned to the claims or implications associated with the event. In the background sections, it should be understood that the scenario is, in most cases, taken from the commission's own assertions. In the first case cited, the commission decided not to publish the incident, but it is relevant to the commission's narrative.
We list 43 events. Had all descriptions been estimated at 0.99 probability of accuracy, 0.9943 is equivalent to about a 65% likelihood of substantive truthfulness, which is a very respectable level of plausibility. However, the cited events cannot measure up to that standard except in three cases. Now suppose we arbitrarily rate all other events at a plausibility measure of 0.95. In that case, we calculate (0.9540)(0.993) = 0.125, or about 12.5% probability that the government is being truthful versus 87.5% probability of a coverup.
However, these ratings are far too generous to the government, as a reading of the events discloses. Collecting the assigned probabilities together yields
(0.993)(0.9510)(0.97)(0.858)(0.83)(0.755)(0.78) =
0.0005303361194787504428381660233787926354219931659698486328125 (according to WolframAlpha). That is, we have 0.053 percent probability that government officials are substantially truthful. Conversely, the probability exceeds 99% that officials are covering up evidence pointing to the real killers.
Now we must be clear that this sort of probability analysis is meant as a means of
a. ranking plausibilitiesThe numbers do not reflect known frequencies and so are qualitatively intended, giving qualitative ratios. So when we say that it looks as though there is less than a one percent probability that the government is being substantially truthful with the public, that's just another way of saying that reasonable people, once having examined all the claims set forth here, will find beyond a reasonable doubt that the government is UNTRUTHFUL.
b. setting an overall plausibility value
On point b, it may be objected that multiplication of numbers associated with independent claims implies frequencies that simply do not exist or, if they do, cannot be ascertained. The reply: just as a ranking system is essentially an analogue of a frequency basis, so the multiplication mimicks what is done for frequencies. As mentioned, there is no claim that the numbers represent anything much beyond degrees of belief.
(This whole matter has been discussed a number of times, including by J.M. Keynes† in his work of philosophy titled A Treatise on Probability [Macmillan 1921]. I cover the issue in my e-book, The Many Worlds of Probability, Reality and Cognition.)
Background: At least a year before 9/11, a top-secret data-mining project had identified Mohamad Atta as a probable member of an al Qaeda cell in the United States. The commission staff did not think the matter worthy of mention. The commission claims that the identification was irrelevant and Pentagon officials have said the project was killed because of legal concerns.
Claims or implications: The identification of Atta ahead of time does not indicate that intelligence officials had advance knowledge of the 9/11 attacks.
We assign a probability of accuracy of 0.9 (or 90%), remembering that we are making our estimates high in favor of the government.
Background: In Sept 1998, CIA chief George Tenet told lawmakers that the CIA knew more about the Bin Laden network than about any other top-tier terror network. The CIA had been highly successful in disrupting al Qaeda's Albania-based terror cells, having captured a number of al Qaeda operatives who were then detained by governments friendly to the CIA. Seized by German police was Abu Hajer, al Qaeda's chief of computer operations and weapons procurement.
Claims or implications:
A. The CIA was unable to turn any of these Qaeda agents for use as CIA double agents, or, even if they did, gained no useful inside information concerning 9/11 preparations.
Probability of accuracy: 0.9
B. The CIA did not obtain enough information from Hajer to penetrate al Qaeda's electronic communications, or al Qaeda took strong electronic security precautions once Hajer was captured.
Probability of accuracy: 0.9
C. The CIA did not control the 9/11 operation through the use of double agents.
Probability of accuracy: 0.9
Background: In late 1999, four jihad volunteers from Germany were selected by Bin Laden as "core members" of the 9/11 plot with "remarkable speed," with no comprehensive training or testing of their military preparedness in al Qaeda training camps or on actual terror operations. Atta was quickly given responsibility for the operation, probably based on his personal character, technical ability and familiarity with western ways.
Claims or implications: Atta and the other three were given a big part in such a complex undertaking almost off-handedly.
Probability of accuracy: 0.85
Background: On Sept. 28, 2000, Israel's Ariel Sharon sparked wide outrage among many Muslims for a much-publicized tour of a disputed Jerusalem religious site. The tour touched off rioting and an intifada among Palestinians and was quickly a source of bitter resentment in the Arab world.
Claims or implications: The U.S. government, though generally aware of a potential big strike by bin Laden on U.S. interests, was not specifically concerned about the month of September as a likely time of reprisal, or, if so, thought the attack would be against Israeli interests.
Probability of accuracy: 0.95
Background: In the late 1990s, the CIA considered means of capturing Bin Laden at his compound near the Kandahar airport. The agency was repeatedly frustrated despite several seemingly plausible opportunities. One argument was that mountain tribesmen, while providing good intelligence on Bin Laden, would not conduct a raid on behalf of the CIA.
Claims or implications: The CIA did not deliberately refrain from nabbing Bin Laden as part of a larger scheme to use al Qaeda as a useful pawn.
Probability of accuracy: 0.95
Background: Several plans to knock out Bin Laden with a cruise missile were rejected.
Claims or implications: The possibility of high civilian casualties was too great for the Clinton White House to accept.
Probability of accuracy: 0.99
Background: The "get bin-Laden unit" in the White House and CIA always rejected the idea of a commando raid by U.S. forces.
Claims or implications: A big concern was the possibility such a raid might fail, as did a failed attempt to rescue U.S. hostages in Iran during President Carter's tenure.
Probability of accuracy: 0.99
Background: A top al Qaeda operative and 9/11 mastermind was Khalid Sheikh Mohammed, who in the 1980s obtained a degree in mechanical engineering from a college in the United States and then joined the anti-soviet jihad in Afghanistan. The CIA was a major bankroller of the mujahideen fighters.
Claims or implications: KSM had no contacts with the CIA during the Russian-Afghan war, or, if so, they were minor and the CIA had no dealings with him later.
Probability of accuracy: 0.95
Background: In March 2000, Atta emailed 31 different U.S. flight schools on behalf of a small group of men from Arab countries who were studying in Germany.
Claims or implications: This email was not brought to the attention of U.S. security authorities, or, if so, the intelligence was lost in the bureaucracy.
Probability of accuracy: 0.95
Background: The attacks of 9/11 were reputedly an evolution of al Qaeda plans to bomb 10 airliners over the Pacific or to use hijacked planes as missiles before or during 2000. The CIA had some knowledge of these plans from Phillipines authorities who had captured KSM's nephew after he bombed a Philippines airliner and a movie theater. The nephew had also been a principle in the 1993 bombing of the World Trade Center.
Claims or implications: The CIA and FBI were failing to "connect the dots."
Probability of accuracy: 0.9
Background: Though al Qaeda had reputedly been responsible for two bombings of U.S. embassies and was known for an eagerness to inflict high casualties, and had reputedly mulled over the idea of coordinated attacks on U.S. jetliners, the terrorists had never yet carried out such a complex, wide-ranging precision operation.
Claims or implications:
A. Al Qaeda went ahead with the operation despite the risks of failure.
Probability of accuracy: 0.9
B. Al Qaeda was unconcerned, perhaps because of religious zealotry, about overplaying its hand and instigating a war against its Taliban hosts.
Probability of accuracy: 0.95
Background: A National Security Agency electronics intercept led the CIA to observe 9/11 hijackers Khalid al Mihdhar and Nawaf al Hazmi at a meeting of terrorists in Kuala Lumpur in January 2000. The agency knew Mihdhar was a terrorist and knew enough to get more information on Hazmi. The pair was tracked by the CIA but reportedly lost on the teeming streets of Bangkok. The CIA's counterterror center told no one outside the unit of the cold trail, the CIA did not register either on the State Department's terror suspect watchlist and the FBI was kept in the dark. As a result, the pair was able to enter and leave the United States several times with no notice. These events occurred at a time when U.S. security services were worried about a major "millenium" terrorist attack in the United States or against U.S. interests.
Claims or implications: Bureaucratic problems and interagency rivalry let slip an opportunity to keep track of people who were likely leads in a "millenium plot" against the United States.
Probability of accuracy: 0.85
Background: Al Qaeda commander Khalid Sheikh Mohammed reportedly told CIA interrogators that he broke the usual security protocols and urged Mihdhar and Hazmi, who were unfamiliar with western culture, to seek help at a southern California mosque upon entry into the United States. The other hijackers, however, were given explicit instructions to melt into the culture and steer clear of mosques and radical Islamic associates.
Claims or implications: Al Qaeda was not only dealing with Arabs, who have a reputation as a rough-hewn lot, but with men who had pledged to martyr themselves. Hence, it was difficult to control them as one might control professional intelligence agents. On the other hand, Atta's "Hamburg group" seemed to take orders relatively well.
Probability of accuracy: 0.75
Background: Mihdhar, while trying to obtain flight training for his suicide mission, became bored with life in America and flew back to Yemen to visit his newborn son. KSM reputedly told CIA interrogators that he then tried to drop Mihdhar from the operation, but Bin Laden overruled him.
Claims or implications: Because of personal qualities or internal al Qaeda politics, Bin Laden carelessly jeopardized an extremely important operation.
Probability of accuracy: 0.75
Background: The housemate who rented a room to Mihdhar and Hazmi had longstanding contacts with the FBI and local police. He reported nothing to authorities about the pair.
Claims or implications: The hijackers were not placed in a "safe house" by federal operatives.
Probability of accuracy: 0.95
Background: Hijacker Jarrah took five overseas trips from the United States, including one to visit his girlfriend in Germany. Various other hijackers went on holiday overseas during 2001.
Claims or implications: Al Qaeda was unworried about exposing operatives to so many opportunities to attract surveillance, or leaders felt they couldn't force a probable martyr to observe security precautions.
Probability of accuracy: 0.75
Background: Zacarias Moussaoui, a supposed back-up hijacker, sent inquiries to Airman Flight School in Oklahoma from London, where he stayed at a dormitory for Islamic men. British security authorities were conducting intensive counterterrorism investigations and operations, the commission has said.
Claims or implications: Moussaoui's inquiry either did not attract the attention of MI5, or, if so, the matter was filed away with no action taken; but if MI5 notified U.S. authorities, the matter was lost in the bureaucracy.
Probability of accuracy: 0.95
Background: Hijacker Hanjour, while living in Arizona in the 1990s, associated with several people who had been subjects of terrorism investigations. Some trained with Hanjour to be pilots. Others had connections to al Qaeda and Afghan training camps. A number of Arab "freedom fighters" with CIA connections lived in the region at that time.
Claims or implications:
A. On returning to America, Hanjour was not "helped" by past association with the CIA and, at any rate, bureaucratic issues spared him surveillance of a type that would have led to exposure of the plot.
Probability of accuracy: 0.85
B. Additionally, his past associations did not cause him to be placed on a State Department watchlist for terror suspects.
Probability of accuracy: 0.7
Background: During an al Qaeda meeting in Spain, Atta mentioned a jetliner attack on a nuclear plant near New York City. The idea was rejected because the airspace around the plant was restricted and the attack plane might get shot down. Other reasons for rejecting the idea: the plant didn't have symbolic value; top al Qaeda leaders hadn't been consulted.
Claims or implications: The plotters were worried about a shootdown near a nuclear plant but not near the Pentagon, White House or Capitol.
Probability of accuracy: 0.75
Background: President Bush was away from the capital at the time of the attack. If we estimate that he normally spends about 50 days outside the capital, the probability he would be absent on Sept. 11 is 50/365, which is equivalent to about 14%.
Claims or implications: Bush's absence does not indicate advance knowledge of the attacks either on his part or on the part of top aides.
Probability of accuracy: 0.99
Background: In 2001, there were numerous warnings of a major terrorist strike in the offing against the United States reaching federal security officials. Warnings include a June 12 CIA report noting that Khalid Sheikh Mohammed was recruiting people to travel to the United States for an al Qaeda strike (a "spectacular" high-casualty attack was forecast for the end of June); on June 25, six separate intelligence reports told of an impending al Qaeda attack; multiple calamitous attacks were expected; on Aug. 6, a presidential daily brief says the FBI was busy with 70 Bin Laden-related terror investigations, the bureau having detected suspicious activity, such as surveillance of federal buildings in Manhattan, inside U.S. borders consistent with preparations for plane hijackings or other types of attacks.
Claims or implications:
A. No one with real power at the National Security Council level knew enough to "get it together" and make sure airport security was beefed up, but simply relied on alerts to the Federal Aviation Agency that were treated in a bureaucratic fashion.
Probability of accuracy: 0.85
B. The FBI had insufficient data to pinpoint Atta and the others, or if so, the intelligence was lost in a bureaucratic maze.
Probability of accuracy: 0.85
Background: In January 2001, a CIA officer established links between Mihdhar and a terrorist involved in the bombing of the USS Cole. But, at this juncture, the agency appears to have made no effort to find Mihdhar and his Kuala Lumpur companion.
Claims or implications: Some CIA unit was not "running" Mihdhar as an agent.
Probability of accuracy: 0.95
Background: The commission disputes the recollections of CIA chief Tenet and CIA counterterror officer Cofer Black that the FBI had access to the identification of Mihdhar as of January 2001. Reportedly, the FBI did not know that Mihdhar had a U.S. visa, and so made no attempt to find him.
Claims or implications: Bureaucratic problems and interagency rivalry prevented the FBI from hunting down a person with strong terrorist ties. The FBI was not acquiescing in a CIA decision to protect one of its assets. [Mihdhar could have had CIA friends at this point without being an active asset.]
Probability of accuracy: 0.85
Background: In mid-May 2001, a CIA officer detailed to an FBI counterterror unit puzzled over where al Qaeda was likely to strike. A database search of those spotted in Kuala Lumpur disclosed Mihdhar's international travels. The database disclosed that Mihdhar had landed at Los Angeles on Jan. 15. For bureaucratic reasons, Mihdhar was not put on a State Dept. terror watchlist -- despite his known terrorist associations -- and so his travels to and from the United States after May went undetected. Had the FBI put him under watch, the entire 9/11 plot is likely to have unraveled.
Claims or implications: The failure to put Mihdhar on a watchlist had nothing to do with his probable past associations with CIA-backed Arab jihadists in Arizona.
Probability of accuracy: 0.8
Background: In June 2001, an FBI analyst posted to the CIA's Bin Laden unit met with FBI agents probing the Cole case in order to pump them for information. She showed surveillance photos, which included imagery of Mihdhar, to her fellow agents but then rebuffed their attempts to learn more about the people in the photos. FBI counterterror agents would probably have tracked Mihdhar to southern California, quite possibly foiling the 9/11 plot, had the analyst not, in a mistaken interpretation of national security rules, refused them the background data. Hence, Mihdhar received a new U.S. visa two days after this meeting.
Claims or interpretations: The analyst did not withhold data that would likely have prevented the 9/11 attacks because of human fallibility and not because she was aware of at least some aspect of a deep-laid plot.
Probability of accuracy: 0.95
Background: In August 2001, a CIA officer with the Bin Laden unit asked an FBI analyst to review all Kuala Lumpur materials one more time. The two women discovered Mihdhar's U.S. entry and exit records and noted that Hazmi had accompanied Mihdhar to Los Angeles in January 2001. They wanted Mihdhar found, thinking Hazmi was no longer in the United States. Both Mihdhar and Hazmi were placed on the terrorist watchlist. However, the FBI analyst lacked agency status and so conveyed a "routine" priority to the FBI's Manhattan field office, which was handling the Cole case, to find Mihdhar. A routine request would get little immediate attention, meaning the Manhattan field office was barely aware of Mihdhar before the 9/11 attacks.
Claims or implications: An FBI employee posted to a top-priority counterterror unit lacked sufficient status to trigger a major manhunt; the fact that such a terrorist was known to authorities at the highest levels of national security does not indicate prior knowledge of the 9/11 attacks.
Probability of accuracy: 0.9
Background: An FBI agent with the Phoenix field office in July 2001 sent a memo to FBI headquarters and to New York field office terrorism agents warning of the likelihood that Bin Laden was sending students to civil aviation schools in America. The agent noted an "inordinate number of individuals of investigative interest" attending such schools in Arizona. He urged a thorough program to check flight schools.
Claims or implications: The warning, which preceded a warning from the Minneapolis field office concerning suspicious flight school activity, fell on deaf bureaucratic ears -- despite the intensive interest of the Cole case squad in New York in Bin Laden's activities and the fact that Washington intelligence units were highly aware that an attack was imminent.
Probability of accuracy: 0.7
Background: On Aug. 15, 2001, the FBI's Minneapolis office initiated an intelligence investigation of Zacarias Moussaoui after his flight school instructor became suspicious of the aggressive, erratic Arab, who seemed uninterested in learning how to fly properly. Moussaoui was unabashed at revealing his jihadist beliefs to an FBI agent and the field office became convinced that he was planning a hijacking, though the bureau did not at that time learn that he had received money from an al Qaeda operative. The field office tried to interest headquarters in the Moussaoui case but the response was desultory. The field office also got caught up in a bureaucratic wrangle that prevented agents from examining Moussaoui's laptop computer, which, as it turned out, contained important evidence. The CIA contacted London about Moussaoui, identifying him as a "possible suicide hijacker" but London was overwhelmed with terrorism inquiries and gave the matter little attention. Still, the Minneapolis field office sent out a general warning, sharply edited at headquarters insistence, to the FAA, followed up by agents giving in-person, detailed oral warnings to FAA officials, but the FAA response was minimal.
Claims or implications: Though Moussaoui was not viewed as a person of significant interest at headquarters, this fact does not indicate that he was a "known quantity," perhaps a pawn in an intelligence game. Also, this "suicide hijacker" alert did not raise alarm bells concerning the Phoenix memo.
Probability of accuracy: 0.75
Background: The FBI's Minneapolis field office wanted to prevent a hijacking and so arranged for the Immigration and Naturalization Service to hold Moussaoui on an immigration violation in preparation for deportation. Neither Bin Laden nor Khalid Sheikh Mohammed, who was running the 9/11 operation, was aware that Moussaoui had disappeared, but even so, al Qaeda spontaneously sent a more reliable suicide pilot to take his place.
Claims or implications: Al Qaeda was so disorganized that it didn't notice that one of its "glory mission" pilots had vanished but so organized that it kept the highly complex plot moving. Moussaoui's flight training was not arranged in advance to provide "evidence" of al Qaeda's responsibility.
Probability of accuracy: 0.7
Background: Two days before Sept. 11, operational chief Atta and another hijacker went to Portland, Me., for no known reason. Then on the fateful day, at 5:58 a.m., the two men flew from the Portland jetport to Boston's Logan International Airport, where they were to hijack American Airlines Flight 11. As it happens, the flight from Portland was late arriving and caused Atta's baggage to be left at Logan, rather than being trasnferred onto AA11.
After the fiery events, the FBI searched baggage at Logan and found Atta's luggage, which contained various items that pointed to al Qaeda, according to contemporary press accounts. In 2004, after the 9/11 commission report was released, an ex-Boston FBI agent told the Boston Globe that the commission had kept silent on the contents of Atta's luggage, which included all the names of the hijackers and other material underscoring the plot. The agent described the contents as the "Rosetta stone" pointing to al Qaeda. His account was verified by a former federal prosecutor, the Globe said.
In October 2001, investigative reporter Seymour M. Hersh is quoted to have written that he had been told by an intelligence official that the contents of Atta's bags had been planted for authorities to find. Even so, the FBI has stuck with this account. The commission's decision to suppress the details of Atta's baggage seems to be a reflection of the credibility of the story. [A copy of Hersh's story was unobtainable via Google or the New Yorker's search engine.]
Claims or implications:
A: Atta was unworried that the entire mission, which relied on near closely timed hijackings, would have been derailed had he and his associate missed their connection at Logan.
Probability of accuracy: 0.7
B: The evidence found in Atta's luggage was not planted there in order to provide a quick accusation against al Qaeda.
Probability of accuracy: 0.7
Background: Atta chose Logan, which is hundreds of miles from New York, to launch strikes against the Trade Center, rather than Newark airport, which is only a few miles from Manhattan. However, Newark was the launchpad for the hijacking of United Airlines Flight 93, which crashed in Pennsylvania. It is possible that two fuel-heavy Los Angeles-bound jets weren't available at Newark and Atta wanted to keep the trade center flights relatively close in time.
Claims or implications: There is nothing especially peculiar about the decision.
Probability of accuracy: 0.95
Background: At Washington's Dulles airport, three hijackers were flagged by a computer program used to profile terror suspects. Two were quizzed because of suspicious behavior, including the fact that one hijacker failed to produce a photo ID.
Claims or implications: Al Qaeda -- in particular operations chief Atta -- was recklessly casual and would overlook ensuring that every hijacker had a photo ID.
Probability of accuracy: 0.7
Background: Altogether, nine of 19 hijackers were identified by airport screenings as security risks. Atta was profiled in Portland; three were profiled at Dulles; and at Logan the others were profiled. But, not expecting suicidal persons, airline security protocols called only for holding a suspect's baggage off the plane until after he had boarded. So all the hijackers were waved through security checkpoints.
Claims or implications: The hijackers were not given the "high sign" by airport security officials controlled by the CIA or other intelligence unit.
Probability of accuracy: 0.85
Background: AA11 dove from about 26,000 feet, making a sharp turnabout and rammed WTC 1 at nearly 500 mph. UA175 made a similar maneuver, banking sharply just before striking WTC2 at some 600 mph. The pilots had never flown jumbo jets and were barely competent in the cockpit, though they had had training on jumbo jet simulators and could fly smaller aircraft. For example, AA11 hijackers supposedly accidently broadcast to other planes an intercom warning to passengers to remain calm. Even so, the pilots showed remarkable prowess at handling the planes and making sure they hit their targets at these high speeds.
Claims or implications: The al Qaeda pilots had learned enough to qualify for this one "stunt" and the planes, whether hijackers were aboard or not, were not operated by Predator-style remote controls from on the ground.
Probability of accuracy: 0.8
Background: Al Qaeda's AA77 pilot, despite poor grades in flight school, performed a stunt with the jumbo jet worthy of the best Air Force fighter pilots. Upon returning the plane to D.C., he dove from 7000 feet to 2200 feet at which height he executed a 330-degree turn (a very sharp loop), aiming the plane for the Pentagon. He gunned the plane to maximum acceleration and then plowed into the Pentagon. This is a difficult maneuver for a fighter jet, let alone a jumbo jetliner. The risk of failing to pull out of such a dive was rather large.
The success of this stunt reportedly prompted President Bush, an experienced pilot, to wonder aloud about the hijacker's ability.
Claims or implications: The Pentagon was not struck by a bomb; or the Pentagon was not struck by a cruise missile; or the Pentagon was not struck by a remotely controlled aircraft, whether fighter plane or AA11.
Probability of accuracy: 0.7
Background: WTC2 collapses less than an hour after UAW175's strike. Nearly everyone below the crash site had cleared the building because they used elevators. WTC1 collapses an hour and a half after being struck by AA11, with thousands still trapped inside. Hours later, another building in the complex, the 47-floor WTC7 collapses. The National Institutes for Standards and Technology admittedly had a difficult time finding computer simulations leading to the collapse of each of the twin towers. The buildings had been designed to withstand jetliner impacts and no major structural steel building anywhere is known to have collapsed due to fire prior to 9/11. The collapse of WTC7 was assigned a "low probability" by investigators for the Federal Emergency Management Agency.
Claims or implications:
A. Neither of the twin towers was brought down by controlled demolition.
Probability of accuracy: 0.85
B. WTC7 was not brought down by controlled demolition.
Probability of accuracy: 0.7
Remotely controlled 9/11 planes?
The government's own research into the collapses of the trade center towers strongly suggests the use of explosives -- despite what the final report claims. Now would plotters have gone to all the trouble to rig the twin towers with explosives unless they were very, very sure that each would be struck by a plane?
Counting on some ill-trained jihadists would be a fairly iffy proposition. Suppose the hijack went awry, or the hijack pilot got cold feet, or got lost, or missed his assigned tower because of the difficulty of the maneuver...
Hence, this leads us to strongly suspect that, whether hijackers were really aboard or not, the planes were handled by remote control from the ground, using Predator-style technology. This seems even more likely considering the amazing high-G maneuver of the plane that (presumably) struck the Pentagon.
Though Americans knew about cruise guided missiles, they hadn't heard of the Pentagon's secret Predator technology until well after 9/11.
† Tending to bolster our desire for a "plausibility scale," we read that J.M. Keynes in his A Treatise On Probability (Macmillan 1921) preferred the concept of propositional truth to that of supposed "events."
With the term “event,” which has taken hitherto so important a place in the phraseology of the subject, I shall dispense altogether. Writers on Probability have generally dealt with what they term the “happening” of “events.” In the problems which they first studied this did not involve much departure from common usage. But these expressions are now used in a way which is vague and ambiguous; and it will be more than a verbal improvement to discuss the truth and the probability of propositions instead of the occurrence and the probability of events.
‡ A case for subjective, though informed, opinion in probability assessment is made by The Subjectivity of Scientists and the Bayesian Approach by S. James Press and Judith M. Tanur (John Wiley 2001).
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