Chapter 9, Problem 98RE

To determine

To find: Probability of getting each number exactly once

Answer to Problem 98RE

The probability that each side appears exactly once is given by 0.0154

Explanation of Solution

Given:

Suppose a six-sided die is tossed six times

Suppose a six-sided die is tossed six times

Since there are 6 possible outcomes in a single toss of a six-sided die

Therefore, when the six-sided die is tossed six times, then the total number of outcomes will be

  $\begin{array}{l}n\left(S\right)=6^6\hfill \\ =6³\times 6³\hfill \\ =216\times 216\hfill \\ =46,656\hfill \end{array}$

Assume that $E$ represents the event that each side appears exactly once

Note that there are six numbers on the die which has to be filled at six places such that each number appears exactly once.

Therefore, the number of elements favorable to the event E

  $\begin{array}{l}n\left(E\right)=6\times 5\times 4\times 3\times 2\times 1\hfill \\ =720\hfill \end{array}$

Thus the probability that each side appears exactly once is given by

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

Put the values to get

  $\begin{array}{l}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\hfill \\ =\frac{720}{46656}\hfill \\ =0.0154\hfill \end{array}$

Hence, the probability that each side appears exactly once is given by 0.0154