Question

If \(P(A)=\dfrac{7}{13}\), \(P(B)=\dfrac{9}{13}\) and \(P(A\cap B)=\dfrac{4}{13}\), then find \(P(A/B)\).

Hint:

P(A/B) = P(A∩B)/P(B).

Answer 1

Step 1: Key Formula or Approach:
Conditional probability is defined as \(P(A/B) = \dfrac{P(A\cap B)}{P(B)}\), valid whenever \(P(B)>0\).

Step 2: Substituting the given values:
\[ P(A/B) = \frac{P(A\cap B)}{P(B)} = \frac{4/13}{9/13} \]

Step 3: Simplifying the fraction:
The \(13\) in the numerator and denominator cancels:
\[ P(A/B) = \frac{4}{9} \]

Final Answer:
\(P(A/B) = \dfrac49\). \[ \boxed{\dfrac49} \]