Find the chance of throwing a total of 3 or 11 with two dice.

Answer

To find the chance of throwing a total of 3 or 11 with 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. Therefore, the total number of outcomes when throwing two dice is:
\[ 6 \times 6 = 36 \]
So, the sample space \( S \) consists of 36 possible outcomes.

2. **Determine the Favorable Outcomes for Total of 3**:
To find the combinations that yield a total of 3:
- The possible pairs are (1, 2) and (2, 1).
- Thus, the favorable outcomes for a total of 3 are:
- (1, 2)
- (2, 1)
- Therefore, there are 2 favorable outcomes for a total of 3.

3. **Calculate the Probability of Getting a Total of 3**:
The probability \( P(A) \) of getting a total of 3 is given by:
\[ P(A) = \frac{\text{Number of favorable outcomes for 3}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18} \]

4. **Determine the Favorable Outcomes for Total of 11**:
To find the combinations that yield a total of 11:
- The possible pairs are (5, 6) and (6, 5).
- Thus, the favorable outcomes for a total of 11 are:
- (5, 6)
- (6, 5)
- Therefore, there are 2 favorable outcomes for a total of 11.

5. **Calculate the Probability of Getting a Total of 11**:
The probability \( P(B) \) of getting a total of 11 is given by:
\[ P(B) = \frac{\text{Number of favorable outcomes for 11}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18} \]

6. **Combine the Probabilities for Total of 3 or 11**:
Since the events of getting a total of 3 and getting a total of 11 are mutually exclusive (they cannot happen at the same time), we can add the probabilities:
\[ P(A \text{ or } B) = P(A) + P(B) = \frac{1}{18} + \frac{1}{18} = \frac{2}{18} = \frac{1}{9} \]

### Final Answer:
The chance of throwing a total of 3 or 11 with two dice is:
\[ \frac{1}{9} \]