Chapter 15.9, Problem 1.4E

To determine

To find: The expected number of heads.

Answer to Problem 1.4E

The expected score is $3.5$ .

Explanation of Solution

Given:

The given information is as given:

The die rolls with faces numbered $1\text{to}6$ .

The possible outcome of a die rolls are given as:

  $\left\{1,2,3,4,5,6\right\}$

The expectation of the score is found by multiplying the score of each simple event by the probability of that event and adding up these products. Here is how the computation looks for the rolls a die with faces number $1\text{to}6$ experiments.

The probability of getting any face of a dieis $\frac{1}{6}$ .

So the expected score is calculated as:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum x\cdot p\left(x\right)}\\ 1\cdot \frac{1}{6}+2\cdot \frac{1}{6}+3\cdot \frac{1}{6}+4\cdot \frac{1}{6}+5\cdot \frac{1}{6}+6\cdot \frac{1}{6}=\frac{21}{6}\\ =3.5\end{array}$

Therefore the expected scoreis $3.5$ .

As it is impossible to roll a $3.5$ on a $6$ -sided die, so we will not ever get this score.