Chapter 12.7, Problem 14PPS

a.

To determine

To find the expected value of one roll of a die.

Answer to Problem 14PPS

The expected value of one roll of a die is $\frac{7}{2}$

Explanation of Solution

Given information: I

The given statement is:

“Multiply each number on a die by the probability of rolling that number. Add these values.”

Calculation:

The probability for rolling each number on a die is $\frac{1}{6}$

The numbers on a die multiplied by the probability of rolling that number is shown in the table:

  

The sum of the values are:

  $\begin{array}{l}\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ =\frac{1+2+3+4+5+6}{6}\\ =\frac{21}{6}\text{ or }\frac{7}{2}\end{array}$

The expected value of one roll of a die is $\frac{7}{2}$

b.

To determine

To find the expected value of the sum of two die.

Answer to Problem 14PPS

The expected value of the sum of number of two die is 7.

Explanation of Solution

Given information: I

The given statement is:

“Multiply each number on a die by the probability of rolling that number. Add these values.”

Calculation:

The probability for rolling each number on a die is $\frac{1}{6}$

The numbers on a die multiplied by the probability of rolling that number is shown in the table:

  

The sum of the values are:

  $\begin{array}{l}\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ =\frac{1+2+3+4+5+6}{6}\\ =\frac{21}{6}\text{ or }\frac{7}{2}\end{array}$

The expected value of sum of number on two dies are:

  $\begin{array}{l}\frac{7}{2}+\frac{7}{2}\\ =\frac{14}{2}=7\end{array}$

Hence, the expected value of the sum of number of two die is 7.