Class CBSE Class 12 Mathematics Probability Q #829
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If\~P(\frac{A}{B})=0\cdot3, P(A)=0\cdot4 and P(B)=0\cdot8, then P(\frac{B}{A}) is equal to :
(A) 0.6
(B) 0.3
(C) 0.06
(D) 0.4
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AI Tutor Explanation

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Step-by-Step Solution

Given: \( P(\frac{A}{B}) = 0.3 \), \( P(A) = 0.4 \), and \( P(B) = 0.8 \).

We know that \( P(\frac{A}{B}) = \frac{P(A \cap B)}{P(B)} \).

So, \( 0.3 = \frac{P(A \cap B)}{0.8} \).

Therefore, \( P(A \cap B) = 0.3 \times 0.8 = 0.24 \).

We need to find \( P(\frac{B}{A}) \), which is given by \( P(\frac{B}{A}) = \frac{P(A \cap B)}{P(A)} \).

Substituting the values, we get \( P(\frac{B}{A}) = \frac{0.24}{0.4} \).

Therefore, \( P(\frac{B}{A}) = 0.6 \).

Correct Answer: 0.6

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formula of conditional probability and Bayes' theorem to find the required probability.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, specifically applying the conditional probability formula and Bayes' theorem to calculate the probability P(B/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 concepts and formulas related to conditional probability, which is a core topic in the probability chapter.

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