It is assume that when they children are born they are equally likely to be boys or girl what is the probability that a family of four children contain three boys and one girl

Answer 1

To find the probability that a family of four children contains three boys and one girl, we can use the binomial probability formula.

The formula for calculating the probability of exactly k successes in n independent Bernoulli trials, where each trial has a probability p of success, is:

P(k) = (n choose k) * (p^k) * ((1 - p)^(n - k))

In this case, the probability of a child being a boy (success) is 1/2 (since they are equally likely to be boys or girls), and the probability of a child being a girl is also 1/2.

Using the formula, we can calculate:

P(3 boys and 1 girl) = (4 choose 3) * (1/2)^3 * (1/2)^(4 - 3)
= 4 * (1/2)^3 * (1/2)
= 4 * 1/8 * 1/2
= 4/16
= 1/4

Therefore, the probability that a family of four children contains three boys and one girl is 1/4.