## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1106: 99

#### Answer

The fractions of outcomes which is less than $5$ is $\frac{2}{3}$.

#### 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 $n\left( S \right)=6$. The event of getting a number less than 5 can be represented by $E=\left\{ 1,2,3,4 \right\}$. There are four outcomes in this event, so $n\left( E \right)=4$. Therefore, the probability of rolling a number less than 5 is: \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{4}{6} \end{align} Thus, the fraction of outcome which is less than $5$ is $\frac{2}{3}$.

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