A normal die is rolled . Calculate the probability that the number on the uppemost face when it stops rolling will be `(` not `5)`

Answer

To solve the problem of finding the probability that the number on the uppermost face of a rolled die is not 5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
A normal die has 6 faces, numbered from 1 to 6. Therefore, the sample space (S) can be represented as:
\[ S = \{1, 2, 3, 4, 5, 6\} \]
The total number of outcomes (n(S)) is 6.

2. **Determine the Favorable Outcomes**:
We need to find the outcomes where the number on the uppermost face is not 5. The favorable outcomes are:
\[ \{1, 2, 3, 4, 6\} \]
Thus, the number of favorable outcomes (n(not 5)) is 5.

3. **Calculate the Probability**:
The probability of an event is calculated using the formula:
\[ P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
Substituting the values we have:
\[ P(\text{not 5}) = \frac{n(\text{not 5})}{n(S)} = \frac{5}{6} \]

4. **Conclusion**:
Therefore, the probability that the number on the uppermost face when the die stops rolling is not 5 is:
\[ P(\text{not 5}) = \frac{5}{6} \]