A die is thrown once . Find
P(a number `gt` 8).

Answer

To solve the problem, we need to find the probability of rolling a number greater than 8 when a die is thrown once.

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When a single die is thrown, the possible outcomes (sample space) are the numbers 1, 2, 3, 4, 5, and 6.
\[ \text{Sample Space} = \{1, 2, 3, 4, 5, 6\} \]

2. **Determine Favorable Outcomes**:
We need to find the outcomes that are greater than 8. However, since the highest number on a standard die is 6, there are no outcomes in the sample space that are greater than 8.
\[ \text{Favorable Outcomes} = 0 \]

3. **Total Outcomes**:
The total number of outcomes when throwing a die is 6 (the numbers 1 through 6).
\[ \text{Total Outcomes} = 6 \]

4. **Calculate 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:
\[ P(\text{Number} > 8) = \frac{0}{6} = 0 \]

### Final Answer:
The probability of rolling a number greater than 8 when a die is thrown once is \( 0 \).

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