Strange math question

The argument is as follows:

Assuming that the gender of each child is independent of the other's, and that only MF are possible genders, labelling the youngest 1 and the eldest 2, the possibility for their genders are as follows:

1 2

M M

M F

F M

F F

in the first case, the father is telling "1 is male", thus ruling out the last two rows; among the remaining cases, 2 has a chance out of two of being female.

However, in the second case the father information is "at least one of 1,2 is male", which only rules out the last row. In the remaining three rows, in two cases Jack's sibling is a female, while in the other it's a male, whence the 1/3 probability

/r/math Thread