And when you don't know, you have to assume it is 50:50. Otherwise you get different answers for different-but-equivalent information.
I am not making an assumption about the data-generating process in any of these questions. The only “assumptions” I make are that the information is true (so yes, the envelope in Q3 matches the family), that the…
Bertrand's Box Paradox, which I wrote about in my own comment, applies to it. The upshot is that probability is not based on which prize placements _could_ lead the current game state, it is the set of all possible game…
Q1: "A family has two children. You're told that at least one of them is a girl. What's the probability both are girls?" Q2: "A family has two children. You're told that at least one of them is a boy. What's the…
And when you don't know, you have to assume it is 50:50. Otherwise you get different answers for different-but-equivalent information.
I am not making an assumption about the data-generating process in any of these questions. The only “assumptions” I make are that the information is true (so yes, the envelope in Q3 matches the family), that the…
Bertrand's Box Paradox, which I wrote about in my own comment, applies to it. The upshot is that probability is not based on which prize placements _could_ lead the current game state, it is the set of all possible game…
Q1: "A family has two children. You're told that at least one of them is a girl. What's the probability both are girls?" Q2: "A family has two children. You're told that at least one of them is a boy. What's the…