To calculate the joint probability $P(A \text{ AND } B)$, we can use the formula:

$P(A \text{ AND } B) = P(B|A) \cdot P(A)$

Where:

• $P(A) = 0.3$ (the probability of event A),
• $P(B|A) = 0.4$ (the conditional probability of event B given A).

Substitute these values into the formula:

$P(A \text{ AND } B) = 0.4 \times 0.3 = 0.12$

So, the joint probability of A and B occurring is:

$P(A \text{ AND } B) = 0.12$

Answer: The joint probability $P(A \text{ AND } B)$ is 0.12.

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Would you like a more detailed explanation? Let me know if you have any questions!

Here are 5 related questions you might find helpful:

1. How do we calculate conditional probabilities?
2. What is the difference between joint probability and marginal probability?
3. How can Bayes' Theorem be used to compute conditional probabilities?
4. What happens when events A and B are independent?
5. What is the formula for the probability of the union of two events?

Tip: Conditional probability is a powerful tool in understanding how one event impacts the likelihood of another event occurring!