Two unbiased dice are thrown . Find the probability that
the total of the numbers on the dice is 8 ,

Answer

To find the probability that the total of the numbers on two unbiased dice is 8, we can follow these steps:

### Step 1: Determine the Sample Space
When two dice are thrown, each die has 6 faces. Therefore, the total number of possible outcomes (sample space) when throwing two dice is:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify Favorable Outcomes
Next, we need to find the combinations of numbers on the two dice that add up to 8. The possible pairs (outcomes) that give a sum of 8 are:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)

Counting these, we find that there are a total of 5 favorable outcomes.

### Step 3: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we found:
\[ P(\text{Sum is 8}) = \frac{5}{36} \]

### Final Answer
Thus, the probability that the total of the numbers on the dice is 8 is:
\[ \frac{5}{36} \]

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