On his TV show, Gordon Ramsay dispenses sage but profane advice (usually in the

Question

On his TV show, Gordon Ramsay dispenses sage but profane advice (usually in the form of suggestions about the staff and menu) to the owners of failing restaurants. He then revisits each of the restaurants one year later to see if they are still open, and talks to the employees. Ramsay finds that among the restaurants that are still open, 95% implemented his advice, and among the restaurants that closed, only 50% implemented his advice. Further, most of the restaurants visited were in pretty bad shape financially, so assume only 40% would have been able to survive another year. Thus, use Bayes Rule to find P(OIA), the probability a restaurant Ramsay visits remains open for another year, given that they implement his advice

Explanation / Answer

P(A) =P(open and implemented advice)+P(closed and implemented advice)

=0.4*0.95+0.6*0.5=0.68

hence P(O|A)=P(open and implemented advice)/P(A)=0.4*0.95/0.68=0.558824

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