If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B \mid A)=1$, then A. $A \subset B$
B. $B \subset A$
C. $B=\phi$
D.$\mathbf{A}=\boldsymbol{\phi}$

Solution:

Answer: A. $A \subset B$

Explanation:

The following information is provided in the question:

$A$ and $B$ are two examples of situations in which,

$P(A) \neq 0$

And, $\mathrm{P}(\mathrm{B} \mid \mathrm{A})=1$

$\therefore P(B \mid A)=\frac{P(B \cap A)}{P(A)}$

$1=\frac{P(B \cap A)}{P(A)}$

$P(A)=P(B \cap A)$

$\therefore A \subset B$