Question

If \(P(A)=\dfrac{7}{11},\ P(B)=\dfrac{9}{11},\ P(A\cap B)=\dfrac{4}{11}\), then \(P(A/B)=\) ?

• A. \(\dfrac{7}{9}\)
• B. \(\dfrac{4}{9}\)
• C. \(1\)
• D. \(\dfrac{13}{22}\)

Hint:

"Given \(B\)" means reduce the sample space to \(B\): probability becomes \(P(\text{both})/P(B)\).

Answer 1

The Correct Option is B

Why use conditional formula: By definition, \[ P(A\mid B)=\frac{P(A\cap B)}{P(B)}. \] Substitute values: \[ P(A\mid B)=\frac{\tfrac{4}{11}}{\tfrac{9}{11}}=\frac{4}{11}\cdot\frac{11}{9}=\frac{4}{9}. \] So, given that \(B\) has occurred, the chance that \(A\) also occurs is \(\dfrac{4}{9}\).