Question

Let A and B be two events such that $P(A) = 0.4$, $P(B) = 0.5$ and $P(A \cap B) = 0.1$. Then
$$P(A \mid B) = ?$$

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{4}{5}$
• D. $\frac{3}{5}$
• E. $\frac{1}{3}$

Hint:

The conditional probability $P(A \mid B)$ is calculated using the formula $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$, where $P(A \cap B)$ is the probability of both events occurring and $P(B)$ is the probability of event $B$.

Answer 1

The Correct Option is D

We are asked to find $P(A | B)$, the conditional probability of $A$ given $B$. The formula for conditional probability is given by: $$P(A | B) = \frac{P(A \cap B)}{P(B)}$$ From the given information: - $P(A) = 0.4$
- $P(B) = 0.5$
- $P(A \cap B) = 0.1$
Substitute the given values into the formula for conditional probability: $$P(A | B) = \frac{0.1}{0.5} = \frac{1}{5}$$ Thus, the correct answer is $\frac{3}{5}$. 
Thus, the correct answer is option (D), $\frac{3}{5}$.