If P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.1, what is P(A | B)?a.0.2b.0.3c.0.5d.0.6

1. Break Down the Problem

To find $P(A | B)$, we can use the definition of conditional probability: $P(A | B) = \frac{P(A \cap B)}{P(B)}$ where:

• $P(A \cap B) = 0.1$
• $P(B) = 0.5$

2. Relevant Concepts

The formula for conditional probability is crucial for this problem. This formula allows us to express the probability of event $A$ occurring given that $B$ has occurred.

3. Analysis and Detail

Substituting the values we have into the formula:

$P(A | B) = \frac{P(A \cap B)}{P(B)} = \frac{0.1}{0.5}$

4. Verify and Summarize

Calculating $\frac{0.1}{0.5}$:

$P(A | B) = 0.2$

Final Answer

The final answer is $P(A | B) = 0.2$. Therefore, the correct option is a. 0.2.