Q686: If A and B are events such that $P(A/B)=P(B/A)\ne0,$ then ...

Class CBSE Class 12 Mathematics Probability Q #686

KNOWLEDGE BASED

UNDERSTAND

1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE

If A and B are events such that $P(A/B)=P(B/A)\ne0,$ then :

(A) $A\subset B$, but $A\ne B$

(B) $A=B$

(D) $P(A)=P(B)$

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Correct Answer: D

AI Tutor Explanation

Step-by-Step Solution

Given: $P(A/B) = P(B/A)$ and $P(A/B) \ne 0$

We know that $P(A/B) = \frac{P(A \cap B)}{P(B)}$ and $P(B/A) = \frac{P(A \cap B)}{P(A)}$

Since $P(A/B) = P(B/A)$, we have $\frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)}$

Since $P(A/B) \ne 0$, it implies that $P(A \cap B) \ne 0$. Therefore, we can safely divide both sides by $P(A \cap B)$

So, $\frac{1}{P(B)} = \frac{1}{P(A)}$, which implies $P(A) = P(B)$

Correct Answer: P(A)=P(B)

AI Suggestion: Option D

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Pedagogical Audit

Bloom's Analysis: This is an UNDERSTAND question because the student needs to comprehend the given conditional probability condition and relate it to the probabilities of events A and B to determine the correct relationship between them.

Knowledge Dimension: CONCEPTUAL

Justification: The question requires understanding the concepts of conditional probability and the relationships between events, rather than recalling specific facts or performing calculations.

Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the understanding of conditional probability, a core concept covered in the textbook.

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