Question

Explain how counting number of girls in five children family can be treated as a binomial experiment. What assumptions are necessary?

Answer 1

This is a binomial experiment and you'll use the binomial probability distribution because:

1. There are two choices for each birth. Either you get a girl or you get a boy. So there are two outcomes to each trial. This is where the "bi" comes from in "binomial" (bi means 2).
2. Each birth is independent of any other birth. The probability of getting a girl is the same for each trial. In this case, the probability is p = 1/2 = 0.5 = 50%
3. There are fixed number of trials. In this case, there are 5 births so n = 5 is the number of trials.

Since all of those conditions above are met, this means we have a binomial experiment.

Some textbooks may split up item #2 into two parts, but I chose to place them together since they are similar ideas.