Puzzles like that one have always seemed dishonest to me. It only makes sense if you start from the conclusion that it's meant to illustrate Bayes rule, and then work backwards to the assumption that the predicate "boy born on a Tuesday" is supposed to be independent of who's being asked about.
But in plain English, ".. At least one of them is a boy born on Tuesday" suggests the speaker is giving a fact that was chosen because it's true of the person spoken about - like if the kids were both chosen on Thursday then that would be the day named. And read that way, the Bayes illustration doesn't stand and the "correct" answer makes no sense.
To make it honest, it should really be worded like: "Mrs. Chance has two children of different ages. You ask whether at least one of them is a boy born on Tuesday, and you are told yes. What is the probability that both of them are boys?" Or am I missing something?
But in plain English, ".. At least one of them is a boy born on Tuesday" suggests the speaker is giving a fact that was chosen because it's true of the person spoken about - like if the kids were both chosen on Thursday then that would be the day named. And read that way, the Bayes illustration doesn't stand and the "correct" answer makes no sense.
To make it honest, it should really be worded like: "Mrs. Chance has two children of different ages. You ask whether at least one of them is a boy born on Tuesday, and you are told yes. What is the probability that both of them are boys?" Or am I missing something?