Final answer:
The probability that a couple with two children will have at least one boy is 0.75 or 75%, which is calculated as the complement of the event that both children are girls.
Step-by-step explanation:
To find the probability that when a couple has two children, at least one is a boy, we must consider all possible combinations of two children: BB (both are boys), BG (first is a boy, second is a girl), GB (first is a girl, second is a boy), and GG (both are girls), assuming boys and girls are equally likely.
Since the probability for each event is the same (1/4 for each combination), we can say that the chance of having no boys (GG) is 1/4. Therefore, the probability of having at least one boy is the complement of having no boys (1 - probability of no boys). This is calculated as:
Probability of at least one boy = 1 - Probability of GG = 1 - 1/4 = 3/4 or 0.75.
Hence, the probability that at least one of the two children is a boy is 0.75 or 75%.