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: 63% of all the franchise stores show a profit the first year; 67% of all the franchise stores show a profit the second year (this includes stores that did not show a profit the first year); however, 81% 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 PO-PCture shuss profit for ist year) 6 P(1) - P (store shop forft for and year) = 0.67 9 PCB(A) = P (shows profit for and your profit for =0.81 d) P(A and B) = P(A x P (BA) = 0,63% 0.8) P(AMB) = 0.5103 e P(ARN B = P(AUB) -P(A) + P(B) -P(AMB) = 0.63+0.67 -0.5103 - 1.3-0.5103 = 0.7897 f) Probability that a new store will not be clord after 2 yeon =P (Ao profit in et 2 years) EXCA =P(AMB) * = 0.5103
i
P (new store will be closed) = P (no profit in both year) = 1- 0.5103 = 0.4897