Question

If A and B are two events in a sample space S such that $P\left(A\right)\ne 0$, then $P\left(\frac{B}{A}\right)=$

• A. $P\left(A\right).P\left(B\right)$
• B. $\frac{P(A\cap B)}{P\left(B\right)}$
• C. $\frac{P(A\cap B)}{P\left(A\right)}$
• D. $P\left(B\right)$

Answer 1

The correct option is C $\frac{P(A\cap B)}{P\left(A\right)}$

$P\left(\frac{B}{A}\right)$ means probability of B given that A has occurred.
So, $P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$
So, C is the correct answer.