Answer to Question #326130 in Statistics and Probability for tya

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:

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