Chapter 12, Problem 21SGR

To determine

The probability for the given case.

Answer to Problem 21SGR

The probability is 0.0609.

Explanation of Solution

Given:

Bob is moving and all of his sports cards are mixed up in the box.

Twelve cards are baseball, eight are football and five are basketball.

The probability for P(1 basketball,2 football)

The total number of the cards is:

  $12+8+5=25$

The number of ways for selecting the 3 balls out of the 25:

  $\begin{array}{l}C\left(25,3\right)=\frac{25!}{3!\left(25-3\right)!}\\ =2300\end{array}$

Now, evaluating the number of ways of selecting 1 basketball card and 2 football cards:

  $C\left(5,1\right)C\left(8,2\right)=\frac{5!}{1!4!}.\frac{8!}{2!6}=140$

Evaluating the probability for selecting 1 basketball and 2 football:

  $\begin{array}{l}P\left(1\text{basketball, 2 football}\right)=\frac{C\left(5,1\right)C\left(8,2\right)}{C\left(25,3\right)}\\ =\frac{140}{2300}\\ =0.0609\end{array}$

Therefore, the probability is 0.0609.