We don’t want to identify them uniquely, we want to know if they are a terrorist.
Even if all terrorists were Muslim, knowing that somebody is Muslim would only increase the probability that they are a terrorist by a factor of four. If there also are non-Muslim terrorists, P(terrorist|Muslim)/P(terrorist) is even less than that.
one bit of information: terrorist or not
“Fifty-fifty, either I win [the lottery] or I don’t.”
A hypothetical in which 50% of the population is terrorists doesn’t sound particularly relevant to the real world. And if the fraction of the population which is purple people is less than 50% (let’s call it p) learning that somebody is a purple person doesn’t only give 1 bit of information, it gives -log2(p) bits, which in order for p to be remotely near the fraction of terrorists in the real world would have to be at least a dozen, I guess.
Even if all terrorists were Muslim, knowing that somebody is Muslim would only increase the probability that they are a terrorist by a factor of four. If there also are non-Muslim terrorists, P(terrorist|Muslim)/P(terrorist) is even less than that.
“Fifty-fifty, either I win [the lottery] or I don’t.”
Can you read?
A hypothetical in which 50% of the population is terrorists doesn’t sound particularly relevant to the real world. And if the fraction of the population which is purple people is less than 50% (let’s call it p) learning that somebody is a purple person doesn’t only give 1 bit of information, it gives -log2(p) bits, which in order for p to be remotely near the fraction of terrorists in the real world would have to be at least a dozen, I guess.