Dice Sum Conditional

List all ordered pairs of dice that sum to 8.

Count how many of those pairs include a 5.

1. 1. Enumerate the sample space

   The ordered pairs summing to 8 are $(2,6),(3,5),(4,4),(5,3),(6,2)$ — 5 outcomes total.

2. 2. Count favorable outcomes

   Of these, $(3,5)$ and $(5,3)$ include a 5, giving 2 favorable outcomes.

3. 3. Conditional probability

   $P(\text{a 5}|\text{sum}=8)=2/5$.

Answer: 2/5