P(B) = 0.5, P(A ∩ B) = 0.3. Find P(A|B).

To find \( P(A|B) \), which is the conditional probability of \( A \) given \( B \), we can use the formula for conditional probability:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Given:
- \( P(A \cap B) = 0.3 \)
- \( P(B) = 0.5 \)

Substitute the values into the formula:

\[
P(A|B) = \frac{0.3}{0.5} = 0.6
\]

Thus, \( P(A|B) = 0.6 \).

Would you like more details or have any questions about this?

Here are 5 related questions to deepen your understanding:
1. What is the meaning of conditional probability in real-world terms?
2. If \( P(A) = 0.7 \), how would you find \( P(B|A) \)?
3. How does the independence of events \( A \) and \( B \) affect \( P(A|B) \)?
4. Can conditional probability be greater than 1? Why or why not?
5. What is the difference between \( P(A \cap B) \) and \( P(A|B) \)?

**Tip:** In probability, the conditional probability tells us how likely one event is, given that another event has already occurred.

Learn how to calculate conditional probability P(A|B) with given values P(B) = 0.5 and P(A ∩ B) = 0.3. This problem demonstrates how to use the formula for conditional probability, making it ideal for students in Grades 9-12 studying basic probability.

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