3.114 A market-research group specializes in providing assessments of the prospects of sites for new children’s toy stores in shopping centers. The group assesses prospects as good, fair, or poor. The records of assessments made by this group were examined, and it was found that for all stores that had annual sales over

$1,000,000, the assessments were good for 70%, fair for 20%, and poor for 10%. For all stores that turned out to be unsuccessful, the assessments were good for 20%, fair for 30%, and poor for 50%. It is known that 60% of new clothing stores are successful and 40% are unsuccessful.

a. For a randomly chosen store, what is the probability that prospects will be assessed as good?

b. If prospects for a store are assessed as good, what is the probability that it will be successful?

c. Are the events “prospects assessed as good”
and “store is successful” statistically independent?

d. Suppose that five stores are chosen at random.
What is the probability that at least one of them will be successful?