In a single throw of two dice , what is the probability of
a total of 12

Answer

To find the probability of obtaining a total of 12 when throwing two dice, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When two dice are thrown, each die has 6 faces. The total number of outcomes when throwing two dice is calculated as:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]
Therefore, the sample space consists of 36 possible outcomes.

2. **List the Favorable Outcomes**:
We need to find the outcomes that result in a total of 12. The only combination that gives a total of 12 is:
\[ (6, 6) \]
This means both dice show a 6. Thus, there is only **1 favorable outcome**.

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 have:
\[ P(\text{total of 12}) = \frac{1}{36} \]

### Final Answer:
The probability of obtaining a total of 12 when throwing two dice is:
\[ \frac{1}{36} \]

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