Question:
If A and B are two events such that P (A) ≠ 0 and P(B|A) = 1, then.
(A) $A \subset B$
(B) $B \subset A$
(C) $B=\Phi$
(D) $A=\Phi$
Solution:
$P(A) \neq 0$ and $P(B \mid A)=1$
$P(B \mid A)=\frac{P(B \cap A)}{P(A)}$
$\mathrm{l}=\frac{\mathrm{P}(\mathrm{B} \cap \mathrm{A})}{\mathrm{P}(\mathrm{A})}$
$P(A)=P(B \cap A)$
$\Rightarrow A \subset B$
Thus, the correct answer is A.
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