Dice Sum of Nine

List the pairs of face values that add to nine.

Divide the count of favorable pairs by the total number of outcomes, $36$.

1. 1. Enumerate favorable pairs

   The ordered pairs summing to $9$ are $(3,6),(4,5),(5,4),(6,3)$, giving $4$ outcomes.

   $$\#\{(a,b):a+b=9\}=4$$

2. 2. Compute the probability

   There are $36$ equally likely ordered outcomes for two dice.

   $$P=\frac{4}{36}=\frac{1}{9}$$

Answer: 1/9