Class CBSE Class 12 Mathematics Probability Q #694
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If E and F are two events such that \(P(E)>0\) and \(P(F)\ne1,\) then \(P(\overline{E}/\overline{F})\) is
(A) \(\frac{P(\overline{E})}{P(\overline{F})}\)
(B) \(1-P(\overline{E}/F)\)
(C) \(1-P(E/F)\)
(D) \(\frac{1-P(E\cup F)}{P(\overline{F})}\)
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Correct Answer: D

AI Tutor Explanation

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Step-by-Step Solution

\(P(\overline{E}/\overline{F}) = \frac{P(\overline{E} \cap \overline{F})}{P(\overline{F})}\)
Using De Morgan's Law, \(\overline{E} \cap \overline{F} = \overline{E \cup F}\)
So, \(P(\overline{E}/\overline{F}) = \frac{P(\overline{E \cup F})}{P(\overline{F})}\)
Since \(P(\overline{E \cup F}) = 1 - P(E \cup F)\), we have
\(P(\overline{E}/\overline{F}) = \frac{1 - P(E \cup F)}{P(\overline{F})}\)

Correct Answer: \(\frac{1-P(E\cup F)}{P(\overline{F})}\)

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to demonstrate comprehension of conditional probability and set operations to manipulate and simplify the given expression.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of concepts related to conditional probability, complementary events, and their relationships. It requires the student to apply the definitions and formulas associated with these concepts to arrive at the correct answer.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding and application of probability concepts as covered in the textbook.

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