# Bayes' Rule with Random Variables

#### jumblebee

##### New Member
Hello! I'm having so much trouble trying to figure out how to do part (b) of the following problem:

The probability that any child in a certain family will have blue eyes is 1/4, and this feature is inherited
independently by di fferent children in the family.
(a) If there are fi ve children in the family and it is known that at least one of these children has blue eyes, what is the probability that at least three of the children have blue eyes?
(b) If it is known that the youngest child in the family has blue eyes, what is the probability that at
least three of the children have blue eyes?

I tried setting it up like this:

P(At least 3 w/ blue eyes | only one w/ blue eyes) = [P(only one w/ blue eyes | at least 3 w/ blue eyes)*P(at least 3 w/ blue eyes)]/P(only one w/ blue)

So I know the probability that at least 3 have blues eyes; using binomial probability formulas, I ended up with 0.1035. I also found the probability of only one child having blue eyes in the same way, and got 0.0791. However, I have no idea how to find P(one w/ blue | at least 3)… am I missing something/setting up the problem wrong?