Question

If $\text{A}$ and $\text{B}$ are two events such that $\text{A ⊆ B,}$then $\text{P(B/A)}$

• A. $0$
• B. $1$
• C. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
• D. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

Answer 1

The correct option is B

$1$

Finding the value of :

Given that, $A\subseteq B$

$\begin{array}{rcl}& & \text{∴A∩B=B∩A}\\ & & \text{=A}\end{array}$

We know that,

$\begin{array}{rcl}\mathbf{\text{P}}\left(\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{$A$}\right.\right)& \mathbf{=}& \mathit{P}\left(B\cap A\right)\mathbf{/}\mathit{P}\left(A\right)\\ & =& P\left(A\right)/P\left(A\right)\\ & =& \mathbf{1}\end{array}$

Hence, Option ‘B’ is Correct.