StatOps

The scenario: Bob tosses two quarters and, looking at them, casually announces that at least one of them is heads. What is the probability that both are heads?

Your first impulse might be to say "50 percent," but think about this: the set of possible outcomes is {(H,H),(H,T),(T,H),(T,T)}. Since at least one of the coins is heads in three of these cases, and only one of them is double heads, does that make it one third? In other words there are two cases in which Bob would say "at least one of them is heads" when the other coin isn't, and only one case where all three are heads.

Or is that the wrong way to think about it? Does order not matter, and all we have to say is that the probability that both are heads is the same as the probability that just one coin, the "other coin," is heads, and the probability is in fact 50 percent?