Tamarack Resorts and Properties is considering opening a skiing area near McCall, Idaho. 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,
P (A1) = 0.40
P (B2) = 0.35
P (B1) = 0.25
P (A1 | B2) = 0.70
P (A1 | B1) = 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?