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My Bayesian Enlightenment

I agree that the nature of that question requires having a mental model of the mathematician, or at least a mental model of mathematicians in general, which for this question we probably don't have.

However, a similar question can more unambiguously be answered with Eliezer's answer of 1/2.

You're at a dinner at a mathematician's house, and he says that he has two kids. A boy walks through the room, and you ask if the boy is his son. He says yes. What is the probability that the other child is a girl?

Harder Choices Matter Less

I wouldn't trust random numbers from people, though. Making random numbers is nigh impossible for the human brain.