An urn contains 12 balls,5 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 getting one success in three draws can be calculated using the hypergeometric distribution:

P(one success) = (5 choose 1) * (7 choose 2) / (12 choose 3) = 0.385

To get two successes, we need to have two ways of choosing which two of the three draws are a success. So the probability of getting two successes is:

P(two successes) = 2 * [ (5 choose 2) * (7 choose 1) / (12 choose 3) ] = 0.3182

Therefore, the answer is B.

An Urn Contains 12 Balls,5 of Which Are Red