At a certain store the manager has determined that20%of customers pay cash and80%of customers pay by debit card. (No other method of payment is accepted, and no one is allowed to pay with both cash and a debit card.) LetMbe the event that a customer pays cash andDis the event that a customer pays by debit card.

Suppose two customers (Al and Betty) come to the store. Explain why it would be reasonable to assume that their choices of payment methods are independent of each other.

A. Al and Betty's payment methods are independent because there are no customers that pay with both cash and debit.

B. No payment methods other than cash and debit are accepted, so Al and Betty's payment methods must be independent.

C. Assuming that Al and Betty do not know each other or associate, there is no reason to believe that one's payment method will influence the other.

D. Any two customers' payment methods are always independent, so it is reasonable to believe that Al and Betty's methods are independent also.

Tree Diagram

/ \

/ \

D= 0.8 M= 0.2

/ \ / \

D=0.8 M= 0.2 D= 0.8 M=0.2

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DD= 0.64 DM= 0.16 MD= 0.16 MM= 0.04

P(D)= 0.8

P(M)= 0.2

P(DD)=0.64

P(DM)=0.16

P(MD)=0.16

P(MM)=0.04

LetSbe the event that both customers use the same method of payment. FindP(S).

LetTbe the event that both customers use different methods of payment. FindP(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods.