Alex White, the current portfolio manager, is examining his portfolio. The portfolio contains 100 stocks that are either value or growth stocks. 40% of the stocks are value stocks. A previous portfolio manager selected 70% of the value stocks and 80% of the growth stocks. What is the probability of selecting a stock at random that is either a value stock or was selected by a previous portfolio manager? A. 28%. B. 76%. C. 88%. D. 16%. Need some help on this…
C 88% Draw the tree. 40% are value stocks. 60% (1-.4) are growth stocks. Or is addition in probability. 40% of the portfolio is value and some of that is selected by the old PM. 60% of the portfolio is growth, and 80% is selected by the old PM. (.6 x .8) .4 + (.6 x .8) = 88%
88% = [((0.4 * 0.7) + (0.6 * 0.8)) + 0.4] - (0.4 * 0.7) there are extra parenthesis in there to follow the steps. To explain further, first you find the probability that the previous manager selected the stocks in the portfolio: ((0.4 * 0.7) + (0.6 * 0.8)). Next you add this to the probaility that the stock is a value stock (given in the problem): + 0.4]. Finally, you subtract out the probability that the stock is a value stock picked by the previous manager (you don’t want to double count): - (0.4 * 0.7).
Great explanation forumreader. Thanks.