An investment firm is thinking of opening a skiing facility in Colorado. It is trying to decide whether to open an area catering to family skiers or to some other group. To help make its decision, it gathers the following information. Let A1 = Family will ski A2 = Family will not ski B1 = Family has children but none in the 8–16 age group B2 = Family has children in the 8–16 age group B3 = Family has no children Then, for this location, P1A12 = 0.40 P1B22 = 0.35 P1B12 = 0.25 P1A1 B22 = 0.70 P1A1 B12 = 0.30

a. Use the probabilities given to construct a joint probability distribution table.

b. What is the probability a family will ski and have children who are not in the 8–16 age group? How do you write this probability?

c. What is the probability a family with children in the 8–16 age group will not ski?

d. Are the categories skiing and family composition independent?