Franchise Stores: Profits Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first 2 years. The accounting office at Wing Foot provided the following information: 65% of all Wing Foot stores show a profit the first year; 71% of all Wing Foot stores show a profit the second year (this includes stores that did not show a profit the first year); however, 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year.

Compute the following:

(a) P(A)

(b) P(B)

(c) P(B | A)

(d) P(A and B)

(e) P(A or B)

(f) What is the probability that a new Wing Foot store will not be closed after 2 years? What is the probability that a new Wing Foot store will be closed after 2 years?