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, 89% of the franchise stores that showed a profit the first year also showed a profit the second year. ?

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, 89% 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 Wing Foot store will not be closed after 2 years?

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

The answers to the question are

(a) P(A) = 0.63

(b) P(B) = 0.73

(c) P( B | A) = 0.89

(d)  P(A and B) =  0.57

(e)  P(A or B)= 0.90

(f)  The probability that a new Wing Foot store will not be closed after 2 years is 0.90

(g) The probability that a new Wing Foot store will be closed after 2 years is 0.1

Step-by-step explanation:

We have, directly from the question

(a) The percentage of stores that show a profit the first year = 63 %,

Therefore P(A) = 0.63

(b) The percentage of stores that show a profit the second year = 73 %,

Therefore P(B) = 0.73

(c)  P( B | A) = The percentage of stores that showed profit the first year and also showed profit the second year which is P (A and B)/P(A) and from the question,  P( B | A) = 0.89

(d) P(A and B) = P( B | A)×P(A) = 0.89 × 0.63 = 0.57 to 2 places of decimal

(e) P(A or B) = P(A) + P(B) - P(A)×P(B) = 0.63 + 0.73 -0.63*0.73 = 0.90

(f)  The probability that a new Wing Foot store will not be closed after 2 years is P(A or B) = 0.90

(g) The probability that a new Wing Foot store will be closed after 2 years is given by P(A or B)' = 1 - 0.90 = 0.10

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