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: Understanding the Concept:
For independent events, knowing that \(B\) has occurred gives no extra information about \(A\); formally \(P(A\cap B)=P(A)\cdot P(B)\) for independent events.

Step 2: Applying the conditional probability formula:
\(P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)\).

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