Chapter 8, Problem 96RE

To determine

To calculate:

The probability that each side appears as exactly once

Answer to Problem 96RE

The probability value to appear each side as exactly once is $0.002$

Explanation of Solution

Given information:

  $\begin{array}{l}n\left(S\right)=6\\ n\left(E\right)=1\end{array}$

Formula used:

The probability value is expressed as:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

The probability value to appear each side as exactly once is given by the following expression:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Put the given data:

  $\begin{array}{l}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ P\left(E\right)=\frac{1}{6}\end{array}$

Know that:

Die is rolled six times, so the probability that each side appears as exactly once is:

  $\begin{array}{l}P\left(E\right)=\frac{6}{6}\cdot \frac{5}{6}\cdot \frac{4}{6}\cdot \frac{3}{6}\cdot \frac{2}{6}\cdot \frac{1}{6}\\ P\left(E\right)=\frac{20}{7776}\\ P\left(E\right)=0.002\end{array}$