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 $940,000 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 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 ( p(b|a) ), if ( p(a)=0.60 ) and ( p(b|\text{not }a)=0.34 ).
0.66
0.47
none of these choices
0.57
0.80

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(B|A)=\frac{P(A\cap B)}{P(A)}\). But we are given that "80% of Wing Foot stores that showed a profit the first year also showed a profit the second year".

Step2: Interpret the given percentage as a conditional probability

The statement "80% of Wing Foot stores that showed a profit the first year also showed a profit the second year" directly gives us the value of \(P(B|A)\). When we say that 80% of the stores that had event \(A\) (profit in the first - year) also had event \(B\) (profit in the second - year), by the definition of conditional probability \(P(B|A)\) (probability of \(B\) given \(A\)), we can write \(P(B|A) = 0.80\).

Answer:

0.80