Find the probability of obtaining a sum 8 in a single throw of two dice.

Answer

To find the probability of obtaining a sum of 8 when throwing two dice, we can follow these steps:

### Step 1: Determine the Total Outcomes
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is:
\[ 6 \times 6 = 36 \]

### Step 2: Identify Favorable Outcomes
Next, we need to find all the combinations of the two dice that result in a sum of 8. We can list them as follows:

1. (2, 6) → 2 + 6 = 8
2. (3, 5) → 3 + 5 = 8
3. (4, 4) → 4 + 4 = 8
4. (5, 3) → 5 + 3 = 8
5. (6, 2) → 6 + 2 = 8

From this, we can see that there are 5 combinations that yield a sum of 8.

### Step 3: Calculate the Probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{5}{36} \]

### Final Answer
Thus, the probability of obtaining a sum of 8 in a single throw of two dice is:
\[ \frac{5}{36} \]

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