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
A
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