Yes, I’m baffled as well. Eliezer says that the prior P(“at least one of them is a boy”|1 boy 1 girl) + P(“at least one of them is a girl”|1 boy 1 girl) = 1, which is nonsensical given that, in fact, the mathematician could have said many other things (given 1 boy 1 girl). But even if this were true, it still doesn’t tell us the probability P(“at least one of them is a boy”|two boys). Regardless of whether she has one boy or two boys, “at least one of them is a boy” is a very unusual thing to say, and it leads me to suppose that she had two children born as boys, one of whom is transgender. But how do I assign a probability to this? No idea.
If the mathematician herself had said “what is the probability that they are both boys?” it becomes more likely that she’s just posing a math problem, because she’s a mathematician… but that’s not how the question was posed, so hmm.
Yes, I’m baffled as well. Eliezer says that the prior P(“at least one of them is a boy”|1 boy 1 girl) + P(“at least one of them is a girl”|1 boy 1 girl) = 1, which is nonsensical given that, in fact, the mathematician could have said many other things (given 1 boy 1 girl). But even if this were true, it still doesn’t tell us the probability P(“at least one of them is a boy”|two boys). Regardless of whether she has one boy or two boys, “at least one of them is a boy” is a very unusual thing to say, and it leads me to suppose that she had two children born as boys, one of whom is transgender. But how do I assign a probability to this? No idea.
If the mathematician herself had said “what is the probability that they are both boys?” it becomes more likely that she’s just posing a math problem, because she’s a mathematician… but that’s not how the question was posed, so hmm.