A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?

Explanation

To solve the problem of finding the conditional probability that the number 5 has appeared at least once when the sum of the numbers appearing on two dice is 8, we can follow these steps:

### Step 1: Identify the Sample Space
When a die is thrown twice, the total number of outcomes is \(6 \times 6 = 36\).

### Step 2: Identify the Event A
Event A is defined as the event where the sum of the numbers on the two dice equals 8. We need to find all the combinations of the two dice that yield this sum:

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