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; 73% of all Wing Foot stores show a profit the second year (this includes stores that did not show a profit the first year); however, 90% 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(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? What is the probability that a new Wing Foot store will be closed after 2 years?

Answer 1

Solution :

A)

P(A) = 0.66 [ANSWER, GIVEN]

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b)

P(B) = 0.73 [ANSWER, GIVEN]

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c)

P(B|A) = 0.90 [ANSWER, GIVEN]

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d)

P(A and B) = P(A) P(B|A) = 0.66*0.90 = 0.594 [ANSWER]

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e)

P(A or B) = P(A) + P(B) - P(A and B) = 0.66 + 0.73 - 0.564 = 0.796 [ANSWER]

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f)

P(not closed) = P(A or B) = 0.796 [ANSWER]

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g)

P(closed) = 1 - P(not closed) = 1 - 0.796 = 0.204 [ANSWER]

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