An urn contains 12 balls, five of which are red. The selection of a red ball is desired and is therefore considered to be a success. If a person draws three balls from the urn, what is the probability of two successes?
A) 0.1591
B) 0.3182
C) 0.6810
D) 0.8409

Question

Quizplus · Accepted Answer

The probability of a success (i.e. selecting a red ball) is P(S) = 5/12. The probability of a failure (i.e. selecting a non-red ball) is P(F) = 7/12. 
To find the probability of two successes, we need to use the binomial probability formula:
P(2 successes) = (3 choose 2) * (5/12)^2 * (7/12)^1
= 3 * (25/144) * (7/12)
= 0.3182
Therefore, the best choice is B.

An Urn Contains 12 Balls, Five of Which Are Red