Question

If \(P(A)=\dfrac12\), \(P(B)=\dfrac13\) and \(A,B\) are independent events, find the value of \(P(A/B)\).

Hint:

For independent events, \(P(A/B)=P(A)\).

Answer 1

Step 1: Direct substitution:
Since \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)P(B)=\dfrac12\times\dfrac13=\dfrac16\).

Step 2: Dividing by P(B):
\(P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{1/6}{1/3}=\dfrac16\times\dfrac31=\dfrac12\).

Final Answer:
\(P(A/B)=\boxed{\dfrac12}\).