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., S 1 ù C1).
(c) Verify that the joint probabilities sum to 1.