An **impossible event** in probability theory refers to an event that cannot occur under any circumstances. Its probability is **zero**. This means that no matter how many times an experiment is performed, the impossible event will never happen. In a probability space, it is represented by the **empty set** (denoted as ∅), as there are no possible outcomes that make the event true.

### Example:
If you roll a standard six-sided die, the probability of rolling a number greater than 6 is an impossible event, as there are no numbers greater than 6 on the die. The probability of this event is 0.

#### Key points about impossible events:
- The probability of an impossible event is always 0.
- An impossible event cannot occur in any scenario within the defined sample space.
- The complement of an impossible event is a **certain event**, which always occurs.

### Example in notation:
- Event: Rolling a number greater than 6 on a six-sided die.
- Probability (P) of event = 0 (impossible event).

Would you like more details on probability events or any other clarification?

Here are 5 questions to extend this concept:
1. What is the difference between an impossible event and a certain event?
2. How is an impossible event represented in a probability distribution?
3. Can an event with a probability of zero occur in some real-world situations?
4. How are impossible events used in defining the boundaries of a probability space?
5. What are some examples of impossible events in real-life scenarios?

**Tip:** Always remember that just because an event has a probability of zero doesn't necessarily mean it's impossible in some continuous cases, like selecting a specific point on a real number line!

Learn the definition of impossible events in probability theory. This concept explains events that cannot occur, represented by a probability of 0, such as rolling a number greater than 6 on a standard die. Discover key points about impossible events, examples, and complementary events in this detailed explanation. Suitable for Grades 6-8 students.

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