Response to the following problem:
The owner of an appliance store is interested in the relationship between the price at which an item is sold (regular or sale price) and the customer's decision on whether to purchase an extended warranty. After analyzing her records she produced the following joint probabilities.
Purchased Extended Warranty Did Not Purchase Extended Warranty
Regular price .21 .57
Sale price .14 .08
a. What is the probability that a customer who bought an item at the regular price purchased the extended warranty?
b. What proportion of customers buy an extended warranty?
c. Are the events independent? Explain.