Question

A particular shoe franchise knows that its stores will not show a profit unless they gross...

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; 73% of all the franchise stores show a profit the second year (this includes stores that did not show a profit the first year); however, 83% 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?

solution:

the given events as follows:

A: new store gross over \$940,000 in first year

B: new store gross over \$940,000 in second year

given probabilities

P(A) = 0.63 , P(B) = 0.73, P(B|A) = 0.83

a) the probability that the new store will gross over \$940,000 in first year is

P(A) = 0.63

b) probability that the new store will gross over \$940,000 in the second year is

P(B) = 0.73

c) probability that the store show a profir second year also show a profit second year is

P(B|A) = 0.83

d) P(A and B) = P(B|A) * P(A)

P(A and B) = 0.83*0.63 = 0.52 (rounded to two decimal places)

e) P( A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.63 + 0.73 - 0.52 = 0.84

f)

proability that a new store will not be closed after two years = P(A or B) = 0.84

g) probability that the new store will be closed after two years = 1 - P(A or B) = 1-0.84 = 0.16