Chapter 13.3, Problem 41AYU

For Problems 41-44, two fair dice are rolled.

Determine the probability that the sum of the faces is 7.

To determine

The probability that the sum of the faces is 7.

Answer to Problem 41AYU

$P\left(sumofthefacesis7\right)=\frac{1}{6}$.

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

$E=\{16,25,34,43,52,61\},n\left(E\right)=6$

$P\left(sumofthefacesis7\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$P\left(sumofthefacesis7\right)=\frac{6}{36}=\frac{1}{6}$