If A and B are two events such that P (A) ≠ 0 and P(B|A) = 1, then.
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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