Chapter 12.5, Problem 18PPS

To determine

To state whether the events are mutually exclusive or not mutually exclusive and find the probability.

Answer to Problem 18PPS

The events are not mutually exclusive and the probability that Ruby chooses a kitten that is female or orange is $\frac{7}{8}\text{ or 87}\text{.5\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Ruby’s cat had $8$ kittens. The litter included $8$ orange females, $8$ mixed-color females, $8$ orange male and $8$ mixed-color males. Ruby wants to keep one kitten. What is the probability that she randomly chooses a kitten that is a female or orange?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The events are not mutually exclusive because she can have a female and orange kitten.

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{female}\right)=\frac{6}{8}\\ \text{P}\left(\text{orange}\right)=\frac{3}{8}\\ \text{P}\left(\text{female and orange}\right)=\frac{2}{8}\\ \text{P}\left(\text{female or orange}\right)=\frac{6}{8}+\frac{3}{8}-\frac{2}{8}\\ \text{P}\left(\text{female or orange}\right)=\frac{7}{8}\text{ or 87}\text{.5\%}\end{array}$

Hence, the events are not mutually exclusive and the probability that Ruby chooses a kitten that is female or orange is $\frac{7}{8}\text{ or 87}\text{.5\%}$ .