To determine if events $A$ and $B$ are mutually exclusive, we need to check if the probability of both events occurring simultaneously, $P(A \cap B)$, is zero. If $P(A \cap B)$ is zero, the events are mutually exclusive.

Given:

• $P(A) = 0.3$
• $P(B) = 0.5$
• $P(A \cap B) = 0.7$

For events $A$ and $B$ to be mutually exclusive, $P(A \cap B)$ must be 0. However, the problem states that $P(A \cap B) = 0.7$, which is not zero.

Therefore, events $A$ and $B$ are not mutually exclusive.

Would you like more details, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. What does it mean for two events to be mutually exclusive?
2. How would the scenario change if $P(A \cap B)$ were 0?
3. Can mutually exclusive events be independent? Why or why not?
4. How do you calculate the probability of the union of two events?
5. What are some real-life examples of mutually exclusive events?

Tip: When dealing with probability questions, always check if events are mutually exclusive by verifying if their intersection is zero.