Class CBSE Class 12 Mathematics Probability Q #831
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If $P(A\cap B)=\frac{1}{8}$ and $P(\bar{A})=\frac{3}{4}$ then $P(\frac{B}{A})$ is equal to :
(A) $\frac{1}{2}$
(B) $\frac{1}{6}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
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AI Tutor Explanation

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Step-by-Step Solution

We are given $P(A \cap B) = \frac{1}{8}$ and $P(\bar{A}) = \frac{3}{4}$. We need to find $P(\frac{B}{A})$.

First, we find $P(A)$ using the complement rule: $P(A) = 1 - P(\bar{A}) = 1 - \frac{3}{4} = \frac{1}{4}$.

Next, we use the formula for conditional probability: $P(\frac{B}{A}) = \frac{P(A \cap B)}{P(A)}$.

Substituting the given values, we get $P(\frac{B}{A}) = \frac{\frac{1}{8}}{\frac{1}{4}} = \frac{1}{8} \times \frac{4}{1} = \frac{4}{8} = \frac{1}{2}$.

Correct Answer: $\frac{1}{2}$

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply the formula for conditional probability and the complement of an event to solve the problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, which involves applying the formula for conditional probability and using the complement rule to find P(A).
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of probability formulas as covered in the textbook.

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