https://file.aiquickdraw.com/mathbot/file/1725678386983mth3p5ws.jpg

The problem in the image is about probability. It states:

"Given that events \(A\) and \(B\) are mutually exclusive events with:
\[ P(A) = \frac{1}{2} \text{ and } P(B) = \frac{1}{3}, \]
what is the value of \( P(A \cap B) \)?"

Since \(A\) and \(B\) are mutually exclusive, this means that the events cannot occur at the same time. For mutually exclusive events, the probability of their intersection is zero:
\[
P(A \cap B) = 0.
\]

So, the correct answer to this problem is \( P(A \cap B) = 0 \), which corresponds to option **A**.

Would you like further clarification or additional details?

Here are five related questions you might find helpful:
1. What is the difference between mutually exclusive events and independent events?
2. How is the probability of two independent events calculated?
3. How do you calculate \(P(A \cup B)\) when events are mutually exclusive?
4. What is the general formula for the probability of the intersection of two events?
5. How does the concept of conditional probability apply to dependent events?

**Tip**: Always verify whether the events are independent or mutually exclusive when dealing with probabilities. This helps in choosing the correct formula.

Diketahui A dan B adalah dua kejadian saling lepas dengan P(A) = 1/2 dan P(B) = 1/3. Nilai dari P(A ∩ B) adalah....

Solve the problem of finding the probability of the intersection of mutually exclusive events A and B with P(A) = 1/2 and P(B) = 1/3. Learn about the concept of mutually exclusive events and the formula P(A ∩ B) = 0.

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