Question

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

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

Answer 1

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

we know that
$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$
From this, we get $P(A\cap B)=P\left(A\right).P\left(\frac{B}{A}\right)$
So, B is the correct answer.