Chapter 12.5, Problem 34HP

To determine

To check if either George or Aliyah is correct.

Answer to Problem 34HP

The probability calculated by Aliyah is correct.

Explanation of Solution

Given information:

The given statement is:

“George and Aliyah are determining the probability of randomly choosing a blue or red marble from a bag of $\text{8}$ blue marbles, $\text{6}$ red marbles, $\text{8}$ yellow marbles and $\text{8}$ white marbles. Is either of them correct? Explain.”

George:

  $\begin{array}{l}\text{P}\left(\text{blue or red}\right)=\text{P}\left(\text{blue}\right)\cdot \text{P}\left(\text{red}\right)\\ \text{P}\left(\text{blue or red}\right)=\frac{8}{26}.\frac{6}{26}\\ \text{P}\left(\text{blue or red}\right)=\frac{48}{476}\text{ or 7\%}\end{array}$

Aliyah:

  $\begin{array}{l}\text{P}\left(\text{blue or red}\right)=\text{P}\left(\text{blue}\right)+\text{P}\left(\text{red}\right)\\ \text{P}\left(\text{blue or red}\right)=\frac{8}{26}+\frac{6}{26}\\ \text{P}\left(\text{blue or red}\right)=\frac{14}{26}\text{ or 54\%}\end{array}$

The events are mutually exclusive as either a blue or a red marble can be chosen at a particular time.

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{blue or red}\right)=\text{P}\left(\text{blue}\right)+\text{P}\left(\text{red}\right)\\ \text{P}\left(\text{blue or red}\right)=\frac{8}{26}+\frac{6}{26}\\ \text{P}\left(\text{blue or red}\right)=\frac{14}{26}\text{ or 54\%}\end{array}$

Hence, the probability calculated by Aliyah is correct.