During a game, Lee rolled two fair six-sided die. To obtain the score, he subtracted the lower number from the higher number. If the numbers shown on the dice were the same, his score is zero.

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.

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