Final answer:
The probability that Mr. and Mrs. Davis will have exactly two boys out of three children is 37.5%, calculated by adding the individual probabilities of the three possible combinations of having two boys.
Step-by-step explanation:
The question asks about the probability that Mr. and Mrs. Davis will have exactly two boys out of three children, assuming that the probability of having a boy is 50% for each child. This is a classic example of a binomial probability problem.
To calculate this, consider there are three possible combinations for having two boys (BBG, BGB, GBB), where B represents a boy and G represents a girl. Since each child is independent of the others in terms of gender, each of these combinations has a probability of (0.5)2 × (0.5) = 0.125 or 12.5%. To find the total probability of having two boys, we add up the probabilities of these combinations: 0.125 + 0.125 + 0.125 = 0.375. Therefore, the probability is 37.5% that they will have exactly two boys.