Question

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 $940,00 its second year. Wing Foot has an administrative policy of closing a new store if it shows a loss in both 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 Wing Foot stores show a profit the second year (this includes stores that did not show a profit the first year); however, 88% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute the following. (Enter your answers to four decimal places.) (a) P(A) (b) P(B) (c) P( BA) (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?

Answer 1

And) Given data a) P(A) = 0.66 b) PLB) = 0.69 c) P(BIA) = 0.88 d) PCA and B) = PlanB) x PCA) = plame) xo(a) - P(B)A)*P(A) = 0.88X0.66 1. PLA) 0.5808 e) Ploor B) = P(m) 4P(B) - planB) = 0.66+0.69 - 0.5808 = 0.7692 As the probability that a new wing store will not be closed after 2 year = P(A or B) = 0.7692 The probability that a new wing foot store will be closed after two years 1- AorB) = 1-0.7692 =0.2308