Question

In a family of 4 children, what is the probability that at least 3 of the children are boys?

answer to 4 decimal places.

Answer 1

Let p = probability of child is boy = 1/2 = 0.5

n = sample size = 4

Also X : number of children are boy

We asked P( X 3)

P( X 3) = P( X = 3) + P( X = 4)

Using binomial probability

P( X = 3) = 4!/3!*1! * (0.5)3*(0.5)1 = 0.2500

P( X = 4) = 4!/0!*4! * (0.5)4*(0.5)0 = 0.0625

P( X 3) = 0.2500 + 0.0625

P( X 3) = 0.3125