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: State the conditional probability definition:
$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}$, valid whenever $P(B)>0$.

Step 2: Substitute, keeping the common denominator explicit:
Both given probabilities share denominator 13, so $P(A\mid B)=\dfrac{4/13}{9/13}=\dfrac{4}{9}$ directly — the 13's cancel.

Final Answer:
\[ \boxed{4/9} \]