Question

in a family of 3 children calculate the probability of having (i) at least one boy (ii) at most 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.