According to the Mortgage Bankers Association, 8% 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?
A) 0.1296
B) 0.3570
C) 0.4926
D) 0.6157

Question

Quizplus · Accepted Answer

The probability that exactly one mortgage is delinquent can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=8$ (the number of trials), $k=1$ (the number of successes), and $p=0.08$ (the probability of success on a single trial). Plugging these values into the formula gives: $P(X=1) = \binom{8}{1}(0.08)^1(0.92)^7 \approx 0.3570$.