A Company Is Considering Producing a New Children's Bar Soap

A company is considering producing a new children's bar soap.A market research firm has told the company that if they perform a survey,a positive survey of a favorable market occurs 65 percent of the time.That is,P(positive survey ∣ favorable market) = 0.65.Similarly,40 percent of the time the survey falsely predicts a favorable market;thus,P(positive survey ∣ unfavorable market) = 0.40.These statistics indicate the accuracy of the survey.Prior to contacting the market research firm,the company's best estimate of a favorable market was 50 percent.So,P(favorable market) = 0.50 and P(unfavorable market) = 0.50.Using Bayes' theorem,determine the probability of a favorable market given a favorable survey.

A) 0.62
B) 0.38
C) 0.53
D) 0.65
E) None of the above