A stock market analyst examined the prospects of the shares of a large number of corporations. When the performance of these stocks was investigated one year later, it turned out that 25% performed much better than the market average, 25%, much worse, and the remaining 50%, about the same as the average. Forty percent of the stocks that turned out to do much better than the market were rated good buys by the analyst, as were 20% of those that did about as well as the market and 10% of those that did much worse. What is the probability that a stock rated a good buy by the analyst performed much better than the average?

Question

Mathematics

Annika Park

27 January, 08:25

A stock market analyst examined the prospects of the shares of a large number of corporations. When the performance of these stocks was investigated one year later, it turned out that 25% performed much better than the market average, 25%, much worse, and the remaining 50%, about the same as the average. Forty percent of the stocks that turned out to do much better than the market were rated good buys by the analyst, as were 20% of those that did about as well as the market and 10% of those that did much worse. What is the probability that a stock rated a good buy by the analyst performed much better than the average?

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Abbie Stark · Answer 1

Solution:Bayes:E1: Stock performs much better than the market averageE2: Stock performs same as the market averageE3: Stock performs worse than the market averageA: Stock is rated a 'Good Buy'Given thatP (E1) =.25, P (E2) =.5, P (E3) =.25, P (A| E1) =.4, P (A| E2) =.2, P (A| E3) =.1Then,

P A EP EP EAP A EP EP A EP EP A EP E=+ + = (.40) (.25).444 (.4) (.25) (.2) (.5) (.1) (.25)