Three percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
A) 0.0003
B) 0.0082
C) 0.0077
D) 0.0008

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 5 (number of trials), k = 2 (number of successes), p = 0.03 (probability of success), and q = 1 - p = 0.97 (probability of failure). The formula for binomial probability is P(X = k) = (n choose k) * p^k * q^(n-k). Plugging in the values: P(X = 2) = (5 choose 2) * (0.03)^2 * (0.97)^3 = 10 * 0.0009 * 0.912673 = 0.0082.

Three Percent of the Customers of a Mortgage Company Default