Originally Posted by

**stevetall** A number of children in the families is 0 - 4. Children and probability are:

0 child = 0.15,

1 = 0.25,

2 = 0.3,

3 = 0.2,

4 = 0.1

Question: What is the probability of this randomly chosen family having exactly 2 girls?

I think we must consider total probability.

- And there are 8 ways that out of four children 1 are girls 4!/(4!*1!)

- 8 ways that out of four children 2 are girls 4!/(3!*2!)

- 8 ways that out of four children 3 are girls 4!(2!*3!)

- 5 ways that out of four children 4 are girls 4!(1!*4!)

Boys and girls do not correlate, they are independent. Probability that there is a girl is 1/2. We choose randomly one family ( which could have 0 or 1 or 2 or 3 or 4 children ).

So two girls in a randomly chosen family has over 30? possibilities

And of these 0-4 children having families are exactly 2 girls

probability is 4/?

Unless this is 5/? - because 0,1,2,3,4 = 5 different alternatives.

Some thoughts;

I think this is not needed: 0.15 * 0.25 * 0.3 * 0.2 * 0.1 ...

BUT: this could be what is needed here: P(B) = P(A) P(B|A) + P(A^c) P(B|A^c)