SOLUTION: 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 wi

Question 1183718: 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) Construct a contingency table base on the statement above.
b) Sketch a tree diagram based on these data.
c) Calculate the probability of all joint probabilities
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
I will do only part (c). (You should be able to do part (b) from the way I wrote the probabilities below.)

P(with shopping cart ∩ card) = 0.56
P(with shopping cart ∩ cash) = 0.16
P(with shopping cart ∩ check) = 0.08

P(without shopping cart ∩ card) = 0.10
P(without shopping cart ∩ cash) = 0.08
P(without shopping cart ∩ check) = 0.02

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