According to the Mortgage Bankers Association, 11% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that exactly one of these mortgages is delinquent?

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Quizplus · Accepted Answer

This is a binomial probability problem where we are looking for the probability of exactly one success (in this case, a delinquent mortgage) in a certain number of trials (eight mortgages). The formula for a binomial probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success on a single trial. Here, n=8, k=1, and p=0.11. Plugging these values into the formula gives us P(X = 1) = (8 choose 1) * (0.11)^1 * (0.89)^7 ≈ 0.3685.