Chapter 11.3, Problem 20HP

To determine

To find: Whether the given statement is true or false.

Answer to Problem 20HP

The given statement is False.

Explanation of Solution

Given:

The given statement is “If you roll a die 10 times, you will roll the expected value at least twice”.

Calculation:

The expected value is calculated as,

  $\begin{array}{c}E\left(X\right)=E\left(X.P\left(X\right)\right)\\ =\left[X_{1}P\left(X_1\right)+\mathrm{........}+X_{n}P\left(X_n\right)\right]\\ =1\left(\frac{1}{6}\right)+2\left(\frac{1}{6}\right)+3\left(\frac{1}{6}\right)+4\left(\frac{1}{6}\right)+5\left(\frac{1}{6}\right)+6\left(\frac{1}{6}\right)\\ =3.5\end{array}$

The dies do not have the number 3.5 which means the number is impossible to roll.

Thus,the given statement is False.