Probability of an impossible event

Answer

To find the probability of an impossible event, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of an Impossible Event**:
- An impossible event is an event that cannot occur under any circumstances. For example, rolling a 7 on a standard six-sided die is an impossible event.

2. **Identify Favorable Outcomes**:
- Since an impossible event cannot happen, the number of favorable outcomes (nf) for this event is 0. This means there are no outcomes that would satisfy the event.

3. **Identify Total Outcomes**:
- The total number of outcomes (nt) can be any number, depending on the scenario. For example, if we are rolling a die, the total outcomes (nt) would be 6 (the numbers 1 through 6).

4. **Use the Probability Formula**:
- The probability (P) of an event is calculated using the formula:
\[ P = \frac{nf}{nt} \]
- Here, nf (number of favorable outcomes) is 0.

5. **Substitute Values into the Formula**:
- Substitute the values into the formula:
\[ P = \frac{0}{nt} \]
- Since nf is 0, the equation simplifies to:
\[ P = 0 \]

6. **Conclusion**:
- Therefore, the probability of an impossible event is always 0.

### Final Answer:
The probability of an impossible event is **0**.