Chapter 13.3, Problem 42AYU

To determine

The probability that the sum of the faces is 11.

Answer to Problem 42AYU

$P\left(sumofthefacesis11\right)=\frac{1}{6}$.

Explanation of Solution

Given:

Two fair dice are rolled.

Formula used:

If $S$ is the sample space of this experiment,

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

Calculation:

The sample space $S=\left\{11,12,13,14,15,16,21,22,23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66\right\},n\left(S\right)=36$.

$E=\{56,65\},n\left(E\right)=2$

$P\left(sumofthefacesis11\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$P\left(sumofthefacesis11\right)=\frac{2}{36}=\frac{1}{18}$