Conditional Probability

Question

522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received. The table below organizes the responses.

satisfied with service not satisfied with services total

Made a purchase 130 494 624

Did not make a purchase 715 183 898

Total 845 677 1522

a. [2 pts] What is the probability that a shopper selected at random made a purchase, given that they were not satisfied with the service? Write your answer as a fraction.

b. [2 pts] What is the probability that a shopper selected at random was not satisfied with the service, given that they made a purchase? Write your answer as a fraction.

Answer 1

Your table is crumbled but it is possible to straightened out. But there was 1522 customers, not 522.

satisfied not satisfied total

purchased 130 494 624

did not purchase 715 183 898

total 845 677 1522

a) What is the probability that a shopper selected at random made a purchase, given that they were not satisfied with the service?

677 people were not satisfied - that is the "given" (second column total), 494 of them made a purchase, so

p=494/677

b) What is the probability that a shopper selected at random was not satisfied with the service, given that they made a purchase?

624 customers made a purchase - that is the "given" (first row), 494 of them were not satisfied

p=494/624