Question

In a family of 3 children, find the probability of having at least one boy.

Answer 1

The probability that each child will be a boy is 1/2.

The probability that each child will be a girl is 1/2.

The probability of no. boys = 1/2 × 1/2 × 1/2 = 1/8

The probability of at least 1 boy = 1 - the probability of no boys.

= 1 - 1/8 = 7/8

or

The number of the possibilities is shown below

Probability of 0 boys = 1/8

Probability of 1 boy = 3 × 1/8 = 3/8

Probability of 2 boys = 3 × 1/8 = 3/8

Probability of 3 boys = 1/8

The probability of at least 1 boy is equal to the probability of 1 or 2 or 3

boys which = 3/8 + 3/8 + 1/8 = 7/8.