A stock market analyst examined the prospects of the shares of a large number of

Question

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 th =e analyst performed much better than the average?

Explanation / Answer

To solve this problem first determine the fraction of the population of the stocks evaluated which were rated good buys. Reducing your percentages to decimals: .25 of better performers x 0.4 rated good = 0.1 of population .5 of average performers x 0.2 rated good = 0.1 of population .25 of worse performers x 0.1 rated good = 0.025 of population where "population" is understood to be the basket of stocks which your analyst evaluated. Adding up the numbers on the right shows 0.225 of rhe population were rated good. The probability that the analyst's "good buy" picks did better than the market is 0.1/0.225 = 0.444.

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