Question

A couple intends to have four children. Assume that having a boy or a girl is an equally likely event. Find the probability that the couple has four children of the same sex.

Answer 1

The probability that a couple has four children of the same sex is 1/8, or approximately 12.5%.

Step-by-step explanation:

To find the probability that a couple has four children of the same sex, we can use the concept of independent events. Each child the couple has can be considered as an independent event with a 50% chance of being a boy and a 50% chance of being a girl.

Since the gender of each child is independent of the others, we can multiply the probabilities of having a boy or a girl for each child. The probability of having four boys is (1/2) * (1/2) * (1/2) * (1/2) = 1/16. Similarly, the probability of having four girls is also 1/16.

Therefore, the total probability that the couple has four children of the same sex (either all boys or all girls) is 1/16 + 1/16 = 1/8, which is approximately 0.125 or 12.5%.