Thread: Probability of a girl?

Please help me understand conditional probability.

Q: Find the probability of a couple having a baby girl when their fourth child is born, given that the first 3 children are girls.

A: I think the answer is 0.5. Because regardless of the situation the probability will always be 0.5 as each event is independent.

How can I solve this problem in terms of P(B|A)=P(A and B)/P(A)

Hello, crazydeo!

Good question!

Q: Find the probability of a couple's fourth child is a girl,
given that their first 3 children are girls.

A: I think the answer is 0.5, because regardless of the situation,
the probability will always be 0.5, as each event is independent.

How can I solve this problem in terms of: .

We want: .


The numerator is: .

The denominator is: .


Therefore: .

Just a comment on the problem--

Both crazydeo and Soroban assume that the genders of the children are (statistically) independent. I think this is very likely true, but it is not automatically so. One can imagine biological mechanisms which would result in non-independence.

(According to this web page

Houghton Mifflin Science for Families: Cricket Connections

there was an article in "Chance" which concluded there is no compelling evidence for non-independence.)