Wing foot is a shoe franchise commonly found in shopping cen

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 theta 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: 66% of all wing Foot stores show a profit the first year; 69% of all foot stores show a profit the second year (this includes stores that did not show a profit the first year); however, 84% of wing foot stores that showed a profit the first year also showed a profit the second year. Compute the following. 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 not be closed after 2 years?

Solution

(a) P(A)= 0.66.

(b) P(B)= 0.69.

(c) P(B | A)= P(A and B)/P(A) = 0.5544/0.66 = 0.84

(d) P(A and B) = P(B|A)*P(A) = 0.84*0.65 = 0.5544

(e) P(A or B)= 0.69

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

P[(A or B)] = 0.69

What is the probability that a new Wing Foot store will be closed after 2 years?

P[(A or B)\'] = 0.31