Question

Keith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 6 have

brake problems. A sample of five trucks is randomly selected. What is the probability that two of those tested have defective brakes?

Answer 1

Favorable outcome

Favorable outcomes are when we choose 2 of 6 trucks with defective brakes and 3 of 9 trucks with good brakes. The total number of possible outcomes is the number of ways we can choose 5 trucks of 15:

$P=\cfrac{\begin{pmatrix}6 \\2\end{pmatrix}\cdot \begin{pmatrix}9 \\3\end{pmatrix}}{\begin{pmatrix}15 \\5\end{pmatrix}}=\\ =\cfrac{6!} {2!\cdot4!} \cdot\cfrac{9!} {3!\cdot6!}\cdot\cfrac{5!\cdot10!} {15!}=\\ =0.4196.$