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.