In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?
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A. B. C. D. E.A
This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(p^r)[q^(n-r)]/r!(n-r)!. Here n = 20, r = 8,p = 0.3 and q = 0.7. Therefore we have 20!(0.3^8)(0.7^12)/8!12! = 0.114.