If A and B are two events such that $P(A

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

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

Options:

$A⊂B$

$B⊂A$

$B=\phi$

$A=\phi$

Correct Answer:

$A⊂B$

Explanation:

The correct answer is Option (1) → $A⊂B$

Given:

$P(B|A) = 1$ and $P(A) \ne 0$

From conditional probability:

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

So,

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

This implies that all outcomes of $A$ are contained in $B$.

Therefore,

$A \subseteq B$