18.1. Let a pair of numbers represent the number of spots of the up-face of the first and second die, respectively. The probability of rolling a 7 is

$$\begin{array}{lll}\hfill {\displaystyle P(\text{roll}\text{a}7)}& {\displaystyle =}\hfill & {\displaystyle P(1,6)+P(2,5)+P(3,4)+}\hfill \\ \hfill & \hfill & {\displaystyle P(4,3)+P(5,2)+P(6,1)}\hfill \\ \hfill & {\displaystyle =}\hfill & {\displaystyle \frac{1}{36}+\frac{1}{36}+\frac{1}{36}+\frac{1}{36}+\frac{1}{36}+\frac{1}{36}}\hfill \\ \hfill & {\displaystyle =}\hfill & {\displaystyle \frac{6}{36}=0.167}\hfill \end{array}$$

The probability of rolling an 11 is

$$\begin{array}{lll}\hfill {\displaystyle P(\text{roll}\text{an}11)}& {\displaystyle =}\hfill & {\displaystyle P(5,6)+P(6,5)=\frac{1}{36}+\frac{1}{36}}\hfill \\ \hfill & {\displaystyle =}\hfill & {\displaystyle \frac{2}{36}=0.056}\hfill \end{array}$$

By Rule D, the probability of rolling a 7 or an 11 is

$$\begin{array}{lll}\hfill {\displaystyle P(\text{roll}\text{a}7\text{or}\text{roll}\text{an}11)}& {\displaystyle =}\hfill & {\displaystyle P(\text{roll}\text{a}7)+P(\text{roll}\text{an}11)}\hfill \\ \hfill & {\displaystyle =}\hfill & {\displaystyle \frac{6}{36}+\frac{2}{36}=\frac{8}{36}=0.222}\hfill \end{array}$$