Wing Foot is a shoe franchise commonly found in shopping centers across the Unit

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 does not show a profit in either of the first 2 years. The accounting office at Wing Foot provided the following information: 69% of all Wing Foot stores show a profit the first year; 69% of all Wing Foot stores show a profit the second year (this includes stores that did not show a profit the first year); however, 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute the following.

(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?

Explanation / Answer

A)

P(A) = 0.69 [ANSWER, GIVEN]

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b)

P(B) = 0.69 [ANSWER, GIVEN]

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c)

P(B|A) = 0.87 [ANSWER, GIVEN]

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d)

P(A and B) = P(A) P(B|A) = 0.69*0.87 = 0.6003 [ANSWER]

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e)

P(A or B) = P(A) + P(B) - P(A and B) = 0.69 + 0.69 - 0.6003 = 0.7797 [ANSWER]

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f)

P(not closed) = P(A or B) = 0.7797 [ANSWER]

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g)

P(closed) = 1 - P(not closed) = 1 - 0.7797 = 0.2203 [ANSWER]

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