Question

If \(P(A)=\dfrac7{13}\), \(P(B)=\dfrac9{13}\) and \(P(A\cap B)=\dfrac4{13}\), then find \(P\left(\dfrac AB\right)\).

Hint:

Use P(A|B) = P(A intersection B) / P(B); the 13-denominators cancel.

Answer 1

Step 1: Recall the conditional probability formula:
\[ P\left(\dfrac AB\right)=\dfrac{P(A\cap B)}{P(B)} \]

Step 2: Substitute the given values:
\[ P\left(\dfrac AB\right)=\dfrac{4/13}{9/13}=\dfrac49 \]

Final Answer:
\[ \boxed{\dfrac49} \]