Question

If \(P(A) = \frac{7}{11}\), \( P(B) = \frac{6}{11} \), and \( P(A \cup B) = \frac{8}{11} \), then \( P(A|B) = \) ?}

• A. \( \frac{3}{5} \)
• B. \( \frac{2}{3} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{5}{6} \)

Hint:

Use \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) to find intersection, then apply \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

The Correct Option is D

We use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \Rightarrow \frac{8}{11} = \frac{7}{11} + \frac{6}{11} - P(A \cap B) \Rightarrow P(A \cap B) = \frac{13}{11} - \frac{8}{11} = \frac{5}{11} \] Then, \[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{5/11}{6/11} = \frac{5}{6} \]