Question

$A$ and $B$ are two events such that $P(A)\ne 0,P(B/A)$ if
(i) $A$ is a subset of $B$
(ii) $A\cap B=\Phi$ are respectively

• A. $0$ and $1$
• B. $1,0$
• C. $1,1$
• D. $0,0$

Answer 1

Answer: (B)

Given, $P(A)\ne 0$
(i) If $A$ is subset of $B$
$\therefore P(A\cap B)=P(A)$
$\therefore P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P(A)}=\frac{P(A)}{P(A)}=1$
(ii) If $A\cap B=\varphi$, then $P(A\cap B)=0$
$\therefore P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P(A)}$
$=\frac{0}{P(A)}=0$