FOUR FAMILIES WITH FOUR CHILDREN EACH. WHAT IS THE PROBABILITY THAT TWO OF THE FAMILES WILL HAVE TWO BOYS AND TWO GIRLS IN ANY ORDER.

Answer 1

Let's look at one family first. This could be thought of as a binomial distribution

let A be the event that a family of 4 has 2 boys and 2 girls

where n = 4

and P(Boy) = P(Girl) = 1/2

so P(A) = ₄C₂ * (1/2)² * (1/2)² = 6/16

Now look at 4 families. Again it is binomial where

n = 4

P(A) = 6/16

P(not A) = 10/16

p = ₄C₂ * (6/16)² * (10/16)² ≈ .330