Your telephone operators receive many different types of calls. Requests for information account for 75% of all calls, while 15% of calls result in an actual order. Also, 10% of calls involve both information requests and order placement.
a. What is the conditional probability that a call generated an order, given that it requested information? (This tells you something about the immediate value to your business of handling information requests.)
b. What is the conditional probability that a call did not request information, given that it generated an order? (This represents the fraction of your orders that were “easy.”)
c. What is the probability that a call generated an order and did not request information? Interpret this number.
d. Why are the answers to parts b and c different?
e. Are the two events “requested information” and “generated an order” independent? How do you know?