it is assumed that when children are born they are equally likely to be boys or girls what is probability that a family of four children contain two boys two girls

Answer 1

To find the probability of a family of four children containing two boys and two girls, we can use the concept of binomial probability.

The probability of a single birth event resulting in a boy is 0.5 (equally likely to be a boy or girl). Therefore, the probability of having two boys and two girls in a four-child family can be calculated using the binomial coefficient formula:

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

where:
n = number of trials (total number of children)
k = number of successes (desired outcome)
p = probability of success (probability of having a boy)

In this case, n = 4 (total number of children), k = 2 (number of boys), and p = 0.5.

P(X=2) = (4 choose 2) * 0.5^2 * (1-0.5)^(4-2)
= (6) * 0.25 * 0.25
= 0.09375

Therefore, the probability that a family of four children contains two boys and two girls is 0.09375 or 9.375%.