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: Write the conditional probability formula and plug in fractions with a common denominator already matching:
$P(A/B)=\dfrac{P(A\cap B)}{P(B)}$, and since both given probabilities already share denominator 13, this becomes a ratio of the numerators directly.

Step 2: Divide numerator by numerator:
$P(A/B)=\dfrac{4/13}{9/13}=\dfrac{4}{9}$, since the $13$s cancel when dividing two fractions with the same denominator.

Final Answer:
$P(A/B)=\dfrac{4}{9}$. \[ \boxed{\dfrac49} \]