Chapter 5.6, Problem 41SE

Of grocery shoppers who have a shopping cart, 70 percent pay by credit/debit card (event C₁), 20 percent pay cash (event C₂), and 10 percent pay by check (event C₃). Of shoppers without a grocery cart, 50 percent pay by credit/debit card (event C₁), 40 percent pay cash (event C₂), and 10 percent pay by check (event C₃). On Saturday morning, 80 percent of the shoppers take a shopping cart (event S₁) and 20 percent do not (event S₂). (a) Sketch a tree based on these data. (b) Calculate the probability of all joint probabilities (e.g., S₁ ∩ C₁). (c) Verify that the joint probabilities sum to 1.