Question

If $A$ and $B$ are two events such that $P\left(A\right)\ne 0$ and $P\left(B|A\right)=1$, then

• A. $A\subset B$
• B. $B\subset A$
• C. $B=\varphi$
• D. $A=\varphi$

Answer 1

The correct option is A $A\subset B$

$P\left(A\right)\ne 0$ and $P\left(B|A\right)=1$
$P\left(B|A\right)=\frac{P(B\cap A)}{P\left(A\right)}$
$1=\frac{P(B\cap A)}{P\left(A\right)}$
$P\left(A\right)=P(B\cap A)$
$\Rightarrow A\subset B$
Thus, the correct answer is A.