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.