## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1106: 100

#### Answer

The fraction of outcomes which is not less than 5 is $\frac{1}{3}$.

#### Work Step by Step

We know that the sample space of equally likely outcomes is $S=\left\{ 1,2,3,4,5,6 \right\}$. There are six outcomes in the sample space, so $n\left( S \right)=6$. And the event of getting a number not less than 5 can be represented by $E=\left\{ 5,6 \right\}$. There are four outcomes in this event, so $n\left( E \right)=2$. Therefore, the probability of rolling a number not less than 5 is: \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{2}{6} \end{align} Thus, the fraction of outcomes which is not less than 5 is $\frac{1}{3}$.

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