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 grow 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 940,000 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 two years. Assume that the accounting office at Wing Foot provided the following information: 60% of all Wing Foot stores show a profit the first year: 73% of all Wing foot shows profit the second year (this includes stores that did not show a profit the first year.) however 80% of wing foot stores that showed a profit the first year also showed a profit the second year.Compute P(B/A), if P(A)=.60 and P(B/not A)=.34

a) none of these

b).47

c).66

d).57

f).80

Explanation / Answer

A be the event that a new wing foot store grosses over $940,000 its first year

P(A) = 0.60

B be the event that a store grosses over 940,000 its second year.

P(B) = 0.73

80% of wing foot stores that showed a profit the first year also showed a profit the second year

P(B given A) =P(B/A) = 0.80

so answer is (f)

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P(B/A) = 0.80 => P(B and A)/P(A) = 0.80

P(B and A) = 0.80*P(A) =0.48

P(not A) = 1-P(A) = 1-0.60 = 0.4

P(B and not A) = P(B)-P(A and B) = 0.73-0.48 = 0.23

P(B/ not A) = P(B and not A)/P(not A) = 0.23/0.4 = 0.57

i solved according to the question let me know if you have issues

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