Compute the Probabilities of Hypergeometric Experiments
-A IRS auditor randomly selects 3 tax returns from 50 returns of which 14 contain errors. What is the probability that none of the returns she selects contains an error
A) 0.3643
B) 0.3732
C) 0.022
D) 0.0186

Question

Quizplus · Accepted Answer

The probability that none of the returns selected contains an error can be calculated using the hypergeometric distribution formula. The formula is: P(X=k) = [(C(m, k) * C(N-m, n-k)) / C(N, n)], where N is the total number of items, m is the number of success items in the population, n is the number of items drawn, and k is the number of observed successes. Here, N=50 (total returns), m=14 (returns with errors), n=3 (returns selected), and k=0 (returns with errors selected). Thus, the probability is calculated as P(X=0) = [(C(14, 0) * C(36, 3)) / C(50, 3)] = (1 * 7140) / 19600 = 0.3643.