Question

I need help with this math question.

In a randomly selected family with two children, excluding multiple births, what is the probability of having two girls?
(Assume a girl is as likely as a boy at each birth.)

Answer 1

I feel like it'd be a 50/50 chance

Answer 2

Well no actually
Because you can have a girl and a boy, two boys, or two girls, so it's be more like 1/3 probability

Answer 3

Probability of having a boy = 1/2
Probability of having a girl = 1/2

The probabilities are independent, meaning that the probability of having a child of either sex is always 1/2 regardless of the sex of the previously born child.

Since the events are independent, you have the following:
\[P(\text{2 girls})=P(\text{girl}\cap\text{girl})=P(\text{girl})P(\text{girl})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\]