Question

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

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

Answer 1

The correct option is B $1,0$

Note that $P\left(B/A\right)=\frac{P(A\cap B)}{P\left(A\right)}$

$\left(i\right)$ If A is subset of B, then $A\cap B=A\Rightarrow P(A\cap B)=P\left(A\right)$

Thus $P\left(B/A\right)=\frac{P\left(A\right)}{P\left(A\right)}=1$

$\left(ii\right)$ If $A\cap B=\Phi$, then $P(A\cap B)=0$

So $P\left(B/A\right)=\frac{0}{P\left(A\right)}=0$