To solve the problem, we need to find the probability of rolling a number greater than 1 on a die, given that only odd numbers can come up.
### Step-by-Step Solution:
1. **Identify the Sample Space**:
When a die is thrown, the possible outcomes are {1, 2, 3, 4, 5, 6}. However, since we are told that only odd numbers can come up, we need to restrict our sample space to the odd numbers.
- **Sample Space (S)**: {1, 3, 5}
2. **Determine the Favorable Outcomes**:
We need to find the outcomes that are greater than 1 from our restricted sample space. The numbers greater than 1 in our sample space {1, 3, 5} are {3, 5}.
- **Favorable Outcomes (F)**: {3, 5}
3. **Count the Outcomes**:
- The total number of outcomes in the sample space (S) is 3 (which are 1, 3, and 5).
- The total number of favorable outcomes (F) is 2 (which are 3 and 5).
4. **Calculate the Probability**:
The probability (P) of an event is given by the formula:
\[
P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}
\]
Substituting the values we found:
\[
P(\text{number greater than 1}) = \frac{2}{3}
\]
### Final Answer:
The probability of rolling a number greater than 1, given that only odd numbers can come up, is \(\frac{2}{3}\).
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