10 John is trying to select fiscally responsible stocks and

10. John is trying to select fiscally responsible stocks, and has narrowed his investment choices down to 5 stocks. Assume that 3 of the stocks will fail, and that John will randomly select 2 stocks to invest in. Assume he cannot invest in the same stock twice. (a) What is the probability that he selects one of the stocks that will fail? (b) What is the probability that both stocks he selects will be failures? (C) What is the expected number of stocks that will fail out of the two that he picked?

Solution

(a) P(neither will fail) = (2/5) * (1/4) = 1/10

P(at least one of the two will fail) = 1 - 1/10 = 9/10

(b) P(both will fail) = (3/5) * (2/4) = 3/10

(c) N = 0 * 1/10 + 2 * 3/10 + 1 * (1 - 1/10 - 3/10) = 1.2