Question

A particular shoe franchise 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 store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,00 its second year. The franchise 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 the franchise provided the following information: 69% of all the franchise stores show a profit the first year; 77% of all the franchise stores show a profit the second year (this includes stores that did not show a profit the first year); however, 85% of the franchise 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(B | A)

(d)    P(A and B)

(e)    P(A or B)

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

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

Answer 1

(a) P(A) = probability that the franchise stores show a profit the first year = 0.69

(b) P(B) = probability that the franchise stores show a profit the second year = 0.77

(c) P(B|A) = 0.85

(d) P(A and B) = 0.69*0.85 = 0.5865

(e) P(A or B) = P(A) + P(B) - P(A and B) = 0.69 + 0.77 - 0.5865 = 0.8735

(f) Required probability that the store will not be closed

= P(A or B) = 0.8735

Required probability that a new store will be closed after 2 years = 1 - P(A or B) = 0.1265