Ok, preasumption, getting a boy or a girl is each 50%

So for the woman we know she does not have 2 girls.
And at least 1 boy.

This makes the woman have these chances for having such kids:

1/3 - B B
1/3 - G B
1/3 - B G
0 - G G (exluded from beginning)

So having 2 Boys is a chance of 1/3

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For the man, we know he has 2 children.
One of them is a boy (one of the slots), but thats unimportant,
as we only care for the other one. (wich is independant)

And for the other child to be a boy it is 1/2 chance.

So the man has 2 boys with a chance of 1/2