> I tell you I have two children, and (at least) one of them is a boy born on a Tuesday. What probability should you assign to the event that I have two boys?
> My initial reaction was that the information about the Tuesday was irrelevant, since at issue was gender, not day of birth. In which case, this was the same problem as the one I just described, and the answer would be 1/3. ... The correct answer to the new puzzle is 13/27, just slightly less than 1/2, and not at all close to 1/3.
This does not feel coherent on a gut level, and smart people seem to have worked it that this is true but: the answer to the new problem is the same regardless of the day of week you are told. Can't you make that inference then that the answer to the original question is actually 1/2?
> My initial reaction was that the information about the Tuesday was irrelevant, since at issue was gender, not day of birth. In which case, this was the same problem as the one I just described, and the answer would be 1/3. ... The correct answer to the new puzzle is 13/27, just slightly less than 1/2, and not at all close to 1/3.
This does not feel coherent on a gut level, and smart people seem to have worked it that this is true but: the answer to the new problem is the same regardless of the day of week you are told. Can't you make that inference then that the answer to the original question is actually 1/2?