Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in
Failed transplants?
A).018
B).037
C).333
D).296

Question

Quizplus · Accepted Answer

The probability of all 3 patients having failed transplants is calculated using combinations. The probability is $\frac{\binom{4}{3}}{\binom{12}{3}} = \frac{4}{220} = 0.018$, where $\binom{4}{3}$ is the number of ways to choose 3 failed transplants out of 4, and $\binom{12}{3}$ is the number of ways to choose any 3 transplants out of 12.

Suppose That 4 Out of 12 Liver Transplants Done at a Hospital