What is the probability that both a couple's first two children will be boys?

To determine the probability that both of a couple's first two children will be boys, we start by considering the probability for a single child. Assuming that the gender of each child is independent and that it is equally likely for a child to be a boy or a girl, the probability of having a boy is 1/2.

For two children, the probability of both being boys can be calculated by multiplying the probabilities for each child.

• The probability of the first child being a boy is 1/2.
• The probability of the second child also being a boy is independently 1/2.

Therefore, the combined probability of both children being boys is:

(1/2) * (1/2) = 1/4.

This shows that the probability that both of the couple's first two children will be boys is indeed 1/4. This is why the correct answer is accurate, as it reflects the fundamental principles of independent events in probability.