What is the probability of an event that is​ impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible?

What is the probability of an event that is​ impossible?

The probability of an impossible event is exactly **0**. An impossible event is one that cannot occur under any circumstances.

### Addressing the Empirical Probability:
When a probability is approximated to be zero based on empirical results, it does not necessarily mean that the event is impossible. Empirical probability is based on observed data or experiments, and if an event has a very low frequency of occurrence, its probability might be close to zero. However, this does not mean the event cannot happen; it simply means that it is extremely unlikely based on the available data.

In summary:
- **Impossible Event**: Probability = 0.
- **Very Unlikely Event (Empirical Probability near 0)**: Not impossible, but highly improbable based on observations.

### Do you want more details or have any questions?

Here are 5 relative questions:
1. What is the difference between theoretical and empirical probability?
2. Can an event with a very low probability ever actually occur?
3. How do you calculate the empirical probability of an event?
4. What are some real-world examples of events with very low probabilities?
5. What are the implications of assuming a probability of zero in practical scenarios?

**Tip**: Always distinguish between theoretical and empirical probabilities; the former is based on mathematical reasoning, while the latter relies on observed data.

Explore the concept of probability and understand the distinction between impossible events and events with very low empirical probability. Learn why the probability of an impossible event is exactly 0 and how empirical probability is based on observed data. Suitable for students in Grades 9-12.

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