在一场游戏中，李掷了两个均匀的六面骰子。为了得出得分，他用较大的数字减去较小的数字。如果骰子显示的数字相同，则他的得分为零。

1. Construct the possibility diagram for the score from two dice

Let the column headings be the number on Die 1 and the row headings be the number on Die 2. For each outcome, score $=$ higher number $-$ lower number.

$$\begin{array}{c|cccccc} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 0 & 1 & 2 & 3 & 4 & 5 \\ 2 & 1 & 0 & 1 & 2 & 3 & 4 \\ 3 & 2 & 1 & 0 & 1 & 2 & 3 \\ 4 & 3 & 2 & 1 & 0 & 1 & 2 \\ 5 & 4 & 3 & 2 & 1 & 0 & 1 \\ 6 & 5 & 4 & 3 & 2 & 1 & 0 \end{array}$$

1. Count outcomes with score 5 and find the probability

There are $36$ equally likely outcomes when two fair six-sided dice are rolled.

A score of $5$ occurs for $(1,6)$ and $(6,1)$ only, so there are $2$ favourable outcomes.

$P(\text{score }5)=\frac{2}{36}=\frac{1}{18}$