it is assumed that when children are born they are equally likely to be boy or girl what is the probability that a family of four children contains three boys and one girl

1 answer

To calculate the probability of a family of four children containing three boys and one girl, we can use the concept of the binomial distribution.

In this case, we want to find the probability of three successes (boys) in four trials (four children). Assuming each child is equally likely to be a boy or a girl, the probability of having a boy is 0.5 (or 1/2), and the probability of having a girl is also 0.5.

We'll use the formula P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (4 in this case), k is the number of successes (3 boys), p is the probability of success (0.5), and C(n, k) is the number of combinations of n items taken k at a time (which can be calculated as n! / (k!(n-k)!)).

Plugging in the values, we have:
P(X = 3) = C(4, 3) * 0.5^3 * (1-0.5)^(4-3)
= 4 * 0.5^3 * 0.5^1
= 4 * 0.5^4
= 4 * 0.0625
= 0.25

Therefore, the probability that a family of four children contains three boys and one girl is 0.25 or 25%.