Maths questions

Question

At a certain store the manager has determined that 40% of customers pay cash and 60% 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.) Let M be the event that a customer pays cash and D is the event that a customer pays by debit card.

Let S be the event that both customers use the same method of payment. Find P(S).

Let T be the event that both customers use different methods of payment. Find P(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.



Answer 1

The probability that both customers pay in cash is 0.4 * 0.4 = 0.16. The probability that both customers pay by debit card is 0.6 * 0.6 = 0.36. The probability that both pay by either cash or debit card is 0.16 + 0.36 = 0.52.

The probability that both customers use different payments = 1 - probability they both use different payments = 1 - 0.52 = 0.48. Or the probability customer one use debit and customer two uses cash is 0.6 * 0.4 = 0.24 and the probability that customer one uses cash and customer two uses debit is 0.4 * 0.6 = 0.24, so the probability that they both use different payments is 0..24 + 0.24 = 0.48.