Question

If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit card. Thirty percent of customers use coupons and 35% of customers pay with debit cards. Given that a customer does not pay with a debit card, the probability that the same customer does not use coupons is ________. A) 0.52 B) 0.60 C) 0.77 D) 0.85

Answer 1

Answer:

A. 0.52

Step-by-step explanation:

Let D be the event that person used Debit card and C b the event that person used coupon.

We have to find the probability of customer does not use coupons given that a customer does not pay with a debit card,

P(C'/D')=P(C')P(D'/C')/[P(C')P(D'/C')+P(D')P(D'/C')]

We are given that P(D)=0.35, P(C)=0.30 and P(D/C)=0.5.

P(D')=1-0.35=0.65

P(C')=1-0.3=0.7

P(D'/C')=0.5.

P(C'/D')=0.7(0.5)/[0.7(0.5)+0.65(0.5)]

P(C'/D')=0.35/[0.35+0.325]

P(C'/D')=0.35/[0.35+0.325]

P(C'/D')=0.35/0.675

P(C'/D')=0.5185=0.52

Thus, the probability of customer does not use coupons given that a customer does not pay with a debit card is 0.52.