Question

$AandB$ are two events such that $P\left(A\right)\ne 0,$ then $P(B/A)$if

$\left(i\right)A$ is a subset of $B$

$\left(ii\right)A\cap B=\varnothing$

• A. $1and1$
• B. $0and1$
• C. $0and0$
• D. $1and0$

Answer 1

The correct option is D

$1and0$

Given: $AandB$ are two events such that $P\left(A\right)\ne 0,$

In mathematics, set$AisasubsetofasetB$ if all elements of A are also elements of B;

We know that, $P\left(\frac{B}{A}\right)$ $=\frac{P(A\cap B)}{P\left(A\right)}$

If $AisasubsetofB$, then $A\cap B=A$

Thus, $P(A\cap B)=P\left(A\right)$

Therefore, $P\left(\frac{B}{A}\right)=\frac{P\left(A\right)}{P\left(A\right)}$ $=1$

Now, if $A\cap B=\varnothing ,thenP(A\cap B)=0$

Hence,$P\left(\frac{B}{A}\right)$$=\frac{0}{P\left(A\right)}$$=0$

Therefore,

$P\left(\frac{B}{A}\right)$ for $A$ is a subset of $B$ is$=1$

$P\left(\frac{B}{A}\right)$ for $A\cap B=\varnothing$ is $=0$

Hence, Option(D) is correct.