When rolling a 6-sided die (D6), if A is the event that we roll an even number, and B is the event that we roll a 2, then what is the set A∩B?

To solve this problem, we need to understand the events \( A \) and \( B \) and how to interpret the intersection of these two events, denoted as \( A \cap B \).

### Definitions:
- **Event A**: Rolling an even number on a 6-sided die. The even numbers on a 6-sided die are \( \{2, 4, 6\} \), so:
  \[
  A = \{2, 4, 6\}
  \]

- **Event B**: Rolling a 2. So:
  \[
  B = \{2\}
  \]

### Intersection of \( A \) and \( B \):
The intersection \( A \cap B \) is the set of outcomes that are in both \( A \) and \( B \). In other words, we look for numbers that are both even and equal to 2.

Since \( B = \{2\} \) is already an even number, the intersection is simply:
\[
A \cap B = \{2\}
\]

### Conclusion:
The set \( A \cap B \) is \( \{2\} \), meaning that the only outcome that satisfies both rolling an even number and rolling a 2 is rolling a 2.

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Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the probability of rolling an even number on a D6?
2. What is the probability of rolling a 2 on a D6?
3. How would you describe the union \( A \cup B \) of events \( A \) and \( B \)?
4. What is the complement of event \( A \)?
5. How do you compute the probability of \( A \cap B \)?

**Tip**: The intersection of two events represents outcomes that are common to both events.

Understand how to find the intersection of events when rolling a 6-sided die. This problem explores set theory and probability by identifying the common outcomes between rolling an even number and rolling a 2. Suitable for students in Grades 6-8.

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