P(A|B)!=P(B|A)

As predicted by a friend over IM this morning, the remark about Timothy McVeigh wannabes probably being in Afghanistan or Iraq right now was wildly misinterpreted as an attack on our troops.

I am second to none in my admiration for the military. I do not think that being in the military makes you more likely to be a nutty, militia-style potential home-grown terrorist. At a guess, there are perhaps a couple hundred people in the United States who would like to take violent action against our government in a frantic attempt to ward off the New World Order. There are about 3 million members of the active and reserve military right now. Even if every single one of our homegrown nuts was a service member, the probability that any member of the military was a potential terrorist would be entirely negligible. Most people who are serving in the military do so for honorable, or at the very least respectable, reasons like wanting to serve their country, or get money for school.

But the probability of A, given B is not the same thing as the probability of B, given A. That's what the notation in the title means. To put it more concretely: the probability that you are Jewish, given that you are a rabbi, is 100%. The probability that you are a rabbi, given that you are Jewish, is a small fraction of 1%.

So even though almost no one in the military is a raving nativist loon, many of the raving nativist loons may be in the military. My understanding is that many serial killers are attracted to law enforcement; similarly, people with fantasies about striking a violent blow against the forces of evil may be seeking vocational education in the armed forces. This is no more a smear against the military than it is a smear against firemen to note that many arsonists seek to join their ranks.