Suppose you heard on the radio a breaking news story: “Shots reported at Fort Hood Army base. Several are dead, many more are wounded. Eyewitnesses claim this is an act of terrorism.” You accept, for now, that the news reports are correct and the shooting was not accidental or, say, the result of a lunatic gone postal.
You ask yourself two questions: (A) Was the terrorist a Muslim, and (B) Your neighbor is a Muslim; is he likely to be a terrorist?
Of course, nobody really asks B, but they do ask questions like it; and a lot of very nervous people assume that it’s being asked and don’t want it to be. Anyway, you want to know A and you’d like to have some idea about B.
You cannot know, without information not yet available, whether A or B are certainly true or false; you can only know they are true or false with some probability.
All probability is conditional on information. And the only information you have now are the news reports and your knowledge of historical terrorist attacks. These facts will not be sufficient to let you calculate an exact probability for A or B, but they will be more than adequate to arrive at a qualitative solution.
For ease, let’s write probabilities like this:
Pr (Terrorist | Muslim ).
This reads, in English, “The probability that a person is a Terrorist given we know that they are a Muslim.” In other words, this is B.
A can be written like this:
Pr (Muslim | Terrorist )
where it reads in English “The probability the person is a Muslim given we know that they are a Terrorist.”
It is crucial to recognize that, in general
Pr (Terrorist | Muslim ) does not equal Pr (Muslim | Terrorist )!
To estimate B, Pr (Terrorist | Muslim ), we count all Muslims and then divide into it the number of Muslims who were Terrorists. This fraction is very small; there are a lot of Muslims and very few of them are Terrorists; that is, it is very unlikely B is true.
To estimate A, Pr (Muslim | Terrorist ), we count up all the Terrorists we have known and divide into it the number of them that were Muslim. This fraction is very large; most, and close to all, for the last thirty-ish years, Terrorists have been Muslim; that is, it is very likely A is true.
Thus, it is not racist and it is rational with the information we have, to conclude A is likely true. But it certainly is racist and not rational to assume your Muslim neighbor is a Terrorist, given just the information we posses (news reports and recent history). Keep this in mind before you respond.
On the other hand, if, in trying to answer B, you were to add information that your neighbor attended the same mosque as the 9/11 hijackers, that he was emailing Al Qaeda operatives, and that he was posting pro-suicide bomber messages on internet discussion groups, then
Pr (Terrorist | Muslim & Emails etc. ) is very high.
To deny this conclusion is the opposite of racism: the act of denial comes from the fear of being called racist, the worst crime there is in the USA. Worse, even, than murder—or treason.
However, these results do not help us with the problem of screening for Terrorists at an airport, or, say, in the ranks of Army personnel. Recall that Pr (Terrorist | Muslim ) is very small. But we must also calculate
Pr (Terrorist | Non-Muslim ),
where “Non-Muslim” means the person is a Jew, or Christian, or Wiccan, or whatever, but is not a Muslim. To calculate it, we count up all Non-Muslims and divide into this the number of them that were Terrorists. This fraction is exceedingly small, near zero.
In screening for Terrorists, we can compute the “risk” ratio, or relative terrorism “risk” of being a Muslim. This is calculated by
Pr (Terrorist | Muslim )
Pr (Terrorist | Non-Muslim )
which is a very small number divided by a number that is near zero, which means the relative risk will be somewhat high.
Using just this information suggests it is rational—and not racist—to prevent terrorism by concentrating screening resources on those soldiers who are Muslims and not, say, on those who are Mormon or Catholic. (The number of Muslim soldiers is also small.)
However, it is obvious that these calculations do not account for the fear of being called a racist, a non-trivial concern with non-trivial consequences. This is one of the only crimes where one is presumed guilty and the accused must prove his innocence.
This explains why Army Honcho George Casey is telling every reporter he can that the Army celebrates diversity and Major Hasan was just a nut and not a Terrorist. Casey knows that admitting to the fear of being called a racist is forbidden.