Two unbiased dice are thrown . Find the probability that
both the dice show the same number .

Answer

To solve the problem of finding the probability that both dice show the same number when two unbiased dice are thrown, 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 calculated as follows:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]
This means the sample space consists of 36 possible outcomes.

2. **List the Favorable Outcomes**:
We need to find the outcomes where both dice show the same number. The pairs that satisfy this condition are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

Thus, there are a total of 6 favorable outcomes.

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:
\[ P(\text{both dice show the same number}) = \frac{6}{36} \]

4. **Simplify the Probability**:
We can simplify the fraction:
\[ P = \frac{6}{36} = \frac{1}{6} \]

### Final Answer:
The probability that both dice show the same number is \( \frac{1}{6} \).

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