Find the probability that the sum of the numbers showing on two dice is 8, given that at least one die does not show five.

Explanation

To solve the problem, we need to find the probability that the sum of the numbers showing on two dice is 8, given that at least one die does not show five. We will denote the events as follows:

- Let \( A \) be the event that at least one die does not show a 5.
- Let \( B \) be the event that the sum of the numbers on the two dice is 8.

We want to find \( P(B | A) \), which is the conditional probability of event \( B \) given event \( A \).

### Step 1: Determine the total outcomes for two dice
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