Chapter 12.5, Problem 30PPS

To determine

To find the probability.

Answer to Problem 30PPS

The probability of randomly choosing a red jelly bean, replacing, randomly choosing another red jelly bean, replacing and then randomly choosing an orange jelly bean is $\frac{125}{5488}\text{ or 2\%}$ .

Explanation of Solution

Given information:

The given statement is:

“A bag contains $10$ red, $6$ green, $7$ yellow and $5$ orange jelly beans. What is the probability of randomly choosing a red jelly bean, replacing, randomly choosing another red jelly bean, replacing and then randomly choosing an orange jelly bean?”

Formula used:

The following formula is used:

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

Calculation :

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{red}\right)=\frac{10}{28}\\ \text{P}\left(\text{another red}\right)=\frac{10}{28}\\ \text{P}\left(\text{orange}\right)=\frac{5}{28}\\ \text{P}\left(\text{red, another red, orange}\right)=\frac{10}{28}\times \frac{10}{28}\times \frac{5}{28}\\ \text{P}\left(\text{red, another red, orange}\right)=\frac{125}{5488}\text{ or 2\%}\end{array}$

Hence, the probability of randomly choosing a red jelly bean, replacing, randomly choosing another red jelly bean, replacing and then randomly choosing an orange jelly bean is $\frac{125}{5488}\text{ or 2\%}$ .