A couple is planning to have three children. What is the probability that:a. All of the children will be girls?b. Two of the children will be boys?c. At least 2 of the children will be girls?d. The couple will have 2 boys at the most?

Sure, let's solve these problems one by one:

a. All of the children will be girls? The probability of having a girl or a boy is 1/2 (assuming equal chances). Since the couple is planning to have three children, the probability that all of them will be girls is (1/2) * (1/2) * (1/2) = 1/8.

b. Two of the children will be boys? There are three scenarios where the couple can have exactly two boys: BBG, BGB, GBB. The probability of each scenario is (1/2) * (1/2) * (1/2) = 1/8. So, the total probability is 3 * 1/8 = 3/8.

c. At least 2 of the children will be girls? This includes three scenarios: GGG, GGB, GBG, BGG. The probability of each scenario is (1/2) * (1/2) * (1/2) = 1/8. So, the total probability is 4 * 1/8 = 1/2.

d. The couple will have 2 boys at the most? This includes four scenarios: GGG, GGB, GBG, BGG, BGB, BBG, GBB. The probability of each scenario is (1/2) * (1/2) * (1/2) = 1/8. So, the total probability is 7 * 1/8 = 7/8.