Eye color, Part I

A husband and wife both have brown eyes but carry genes that make it possible for their children to have brown eyes (probability \({{params.c1}}\)), blue eyes (\({{params.c2}}\)), or green eyes (\({{params.c3}}\)).

Part 1

What is the probability the first blue-eyed child they have is their third child? Assume that the eye colors of the children are independent of each other.

Part 2

On average, how many children would such a pair of parents have before having a blue-eyed child?

Part 3

For the previous part, what is the standard deviation of the number of children they would expect to have until the first blue-eyed child?

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.