Class CBSE Class 12 Mathematics Probability Q #693
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If \(P(A\cup B)=0.9\) and \(P(A\cap B)=0\cdot4,\) then \(P(\overline{A})+P(\overline{B})\) is:
(A) 0.3
(B) 1
(C) 1.3
(D) 0.7
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Correct Answer: D

AI Tutor Explanation

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Step-by-Step Solution

We are given \(P(A\cup B)=0.9\) and \(P(A\cap B)=0.4\). We need to find \(P(\overline{A})+P(\overline{B})\).

We know that \(P(A\cup B) = P(A) + P(B) - P(A\cap B)\).

So, \(0.9 = P(A) + P(B) - 0.4\).

Therefore, \(P(A) + P(B) = 0.9 + 0.4 = 1.3\).

We also know that \(P(\overline{A}) = 1 - P(A)\) and \(P(\overline{B}) = 1 - P(B)\).

So, \(P(\overline{A}) + P(\overline{B}) = (1 - P(A)) + (1 - P(B)) = 2 - (P(A) + P(B))\).

Substituting the value of \(P(A) + P(B)\), we get:

\(P(\overline{A}) + P(\overline{B}) = 2 - 1.3 = 0.7\).

Correct Answer: 0.7

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formulas of probability and set theory to find the value of the given expression.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding of the concepts of union, intersection, and complements of events in probability. The student needs to know the formulas related to these concepts to solve the problem.
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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