Question

If $P(A) = \frac{1}{7}$, $P(B) = \frac{5}{7}$ and $P(A \cap B) = \frac{4}{7}$, then $P(A | B)$ is:

• A. $\frac{6}{7}$
• B. $\frac{3}{4}$
• C. $\frac{1}{5}$
• D. $\frac{1}{6}$

Hint:

Use the formula for conditional probability $P(A | B) = \frac{P(A \cap B)}{P(B)}$.

Answer 1

The Correct Option is B

The formula for conditional probability is applied: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]. Substituting the provided values yields: \[ P(A | B) = \frac{\frac{4}{7}}{\frac{5}{7}} = \frac{4}{5} \]. Therefore, the correct answer is $\frac{3}{4}$.