A family has two children. Find the probability that both are girls given that at least one one is a winter-born girl.
I understand all the steps in the solution below except one: "To compute the numerator, use the fact that "both girls, at least one winter girl" is the same event as "both girls, at least one winter child." How does this hold? Doesn't conditioning on knowing that one is a girl make the probability that both are girls higher than the case in which we just condition on season?
Best Answer
"Both girls, one winter girl" means that both children are girls, and out of those two girls, one of them must be a winter girl.
"Both girls, one winter child" means that both children are girls, and out of those two girls, one of them must be a winter child, irrespective of whether that winter child is a boy or a girl.
In the numerator, both children have to be girls, and the winter child is one of those two children, so the winter child must be a girl.
Therefore, the two situations are equivalent.
I hope this explanation helped; if you have any more doubts, feel free to comment on this answer.