Chapter 13.10, Problem 29HP

To determine

The probability of the dale and Shannon of rolling difference $0$ and $1$ on two number cubes so explain it.

  

Answer to Problem 29HP

The probability of the Shannon is correct.

Explanation of Solution

Given:

  

Calculation:

The sample of the rolling dice as follows:

  $S=\left\{\begin{array}{l}\left(1,1\right)=0,\left(1,2\right)=1,\left(1,3\right)=2,\left(1,4\right)=3,\left(1,5\right)=4,\left(1,6\right)=5\\ \left(2,1\right)=1,\left(2,2\right)=0,\left(2,3\right)=1,\left(2,4\right)=2,\left(2,5\right)=3,\left(2,6\right)=4\\ \left(3,1\right)=2,\left(3,2\right)=1,\left(3,3\right)=0,\left(3,4\right)=1,\left(3,5\right)=2,\left(3,6\right)=3\\ \left(4,1\right)=3,\left(4,2\right)=2,\left(4,3\right)=1,\left(4,4\right)=0,\left(4,5\right)=1,\left(4,6\right)=2\\ \left(5,1\right)=4,\left(5,2\right)=3,\left(5,3\right)=3,\left(5,4\right)=1,\left(5,5\right)=0,\left(5,6\right)=1\\ \left(6,1\right)=5,\left(6,2\right)=4,\left(6,3\right)=3,\left(6,4\right)=2,\left(6,5\right)=1,\left(6,6\right)=0\end{array}\right\}$

So out of the $36$ possible outcomes $6$ has the difference and $10$ have zero difference. So,the required probability is,

  $\begin{array}{l}P\left(difference0or1\right)=\frac{10}{36}+\frac{6}{36}\\ P\left(difference0or1\right)=\frac{16}{36}\end{array}$

So Shannon is correct.

Conclusion:

Hence, the probability of the Shannon is correct.