Wing Foot Is a Shoe Franchise Commonly Found in Shopping $$P ( B \mid \mathbf { A } )$$

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 $940,000 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: 56% of all Wing Foot stores show a profit the first year; 71% of all Wing Foot store show a 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 , if and . $$P ( B \mid \mathbf { A } )$$ $P ( A ) = 0.56$ $$P ( B \mid \text { not } \mathrm { A } ) = 0.37$$

A) 0.66
B) 0.80
C) 0.52
D) 0.63
E) none of these choices