# Of Muslim terrorists and terrorist Muslims

##### The Boston manhunt came to an end when the police arrested the second Boston Marathon bomber late Friday night. It is likely to be an isolated incident.

Having been a resident of Boston around Sept. 11, I am more worried about the effect of the bombings on the American psyche. Two men were removed from a Boston-Chicago flight on April 16 for speaking Arabic after several passengers returning from the marathon complained.

I did not get thrown off my Paris-Boston flight a few days after Sept. 11, but I was prone to quite a few “random” checks at airports afterwards. I even got close to getting arrested once in Hawaii’s Big Island after the ticket lady got jittery when I started speaking Turkish with a friend.

Maybe authorities are right to be vigilant? After all, all terrorists are Muslims, right? You could dispute the validity of that claim – the Oklahoma City bomber was certainly not a Muslim. But that’s very different from saying that all Muslims are terrorists. In fact, 48 jihadist plots failed since Sept. 11 thanks to information provided by Muslims. However, these two statements are also related, at least mathematically.

One of the most useful theorems in statistics is Bayes’ Law, which is a simple formula for conditional probabilities. In our case, it states that the ratio of the probability of being a Muslim given one is a terrorist to the probability of being a terrorist given one is a Muslim is equal to the ratio of the probability of being a Muslim to the probability of being a terrorist.

Since the marathon bombers were homegrown, we can plug in the numbers for the United States: There are 6.6 million Muslims in the U.S., making up 2.1 percent of the population. Obviously, no one knows the number of people in the country planning terrorist acts, but I have seen several reports guesstimating a figure of around 500, which would make the probability of being a terrorist at 0.00017 percent. Dividing the first number by the second reveals that it is 13,091 times more likely that a terrorist is a Muslim than a Muslim a terrorist.

But what is the probability that someone is a terrorist given he is a Muslim? Even under the extreme scenario that all terrorists are Muslims, it is 0.0076 percent. You can refine this analysis a bit, by excluding females for example, but the probability will not increase by a lot.

What if you substituted killer with terrorist and gun owner with Muslim? As a devout supporter of gun control, I did not like it a bit when I realized my math seemed to justify the defeat of gun control legislation in the U.S. Senate on April 18. You may argue that without any guns, there would be no murders by guns. But similarly, if you ended up putting all Muslims in a concentration camp, as in the disturbing movie The Siege, there would be no jihadist terrorism in the U.S.

It is just a matter of which you think is more humane. Given the state of things, I am not sure how some American senators would answer this seemingly obvious question.