Special topics in probability theory and mathematical statistics;

There is something wrong with the interpretation of 1 building, which means that the first child is a girl by default.

The correct solution should be to use the definition of conditional probability in probability theory:

First, use A to indicate that there is at least one girl in the event, and use B to indicate that there is at least one boy in the event.

Then what we need to calculate is the probability of event B when event A is known, that is, P(B|A).

According to the definition of conditional probability, P(B|A)=P(AB)/P(A).

Calculate P(AB) and P(A) respectively, as follows:

The opposite event of A is that all three children are boys, and the probability is (1/2) 3 = 1/8, so P (a) =1-1/8 = 7/8;

And AB means there is at least one boy and at least one girl. The opposite event is that there is no boy or girl, that is, all boys or girls. Its probability is (1/2) 3+(1/2) 3 =1/4, so P (AB) = 65438. .

Replace the formula P(B|A)=P(AB)/P(A), namely P(B|A)=6/7.