Hello, dagmary!

Suppose that a family has exactly n children (n ≥ 2).

Assume that the probability that any child will be a girl is ½ and that all births are independant.

Given that the family has at least one girl,

determine the probability that the family has at least one boy.

Bayes' Theorem: .

The opposite of "at least boy and at least girl" is "no boysorno girls."

. .

. .

Then: .

. . . Hence: .

The opposite of "at least one girl" is "no girls".

. .

Hence: .

Therefore: .