Chapter 3.6, Problem 26E

In Exercises $25$ and $26$, use the following information. To determine what effect the salespeople had on purchases, a department store polled $700$ shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, $125$ were happy with the service and $111$ were not. Of those who had made no purchase, $148$ were happy with the service and $316$ were not.

a. If $H$ is the event that a shopper was happy with the purchase and $P$ is the event that a shopper made a purchase, express the probability that a shopper who was unhappy with the service had not made a purchase in terms of $H$ and $P$. Do no calculations; your answer should look something like “ $p$ ( $A$ and $B$).”

b. Find the probability that a shopper who was unhappy with the service had not made a purchase. Round off the nearest hundredth. What can you conclude?