Class CBSE Class 12 Mathematics Probability Q #830
COMPETENCY BASED
APPLY
1 Marks 2023 MCQ SINGLE
18. The probability that A speaks the truth is $\frac{4}{5}$ and that of B speaking the truth is $\frac{3}{4}$. The probability that they contradict each other in stating the same fact is :
(A) $\frac{7}{20}$
(B) $\frac{1}{5}$
(C) $\frac{3}{20}$
(D) $\frac{4}{5}$
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Step-by-Step Solution

Let A be the event that A speaks the truth, and B be the event that B speaks the truth.

Given: P(A) = 4/5, P(B) = 3/4

Therefore, P(A') = 1 - P(A) = 1 - 4/5 = 1/5, and P(B') = 1 - P(B) = 1 - 3/4 = 1/4

The probability that they contradict each other is when A speaks the truth and B lies, or A lies and B speaks the truth.

P(contradiction) = P(A and B') + P(A' and B) = P(A) * P(B') + P(A') * P(B) (since A and B are independent)

P(contradiction) = (4/5) * (1/4) + (1/5) * (3/4) = 4/20 + 3/20 = 7/20

Correct Answer: 7/20

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply their understanding of probability and conditional probability to solve a problem. They need to use the given probabilities to calculate the probability of a specific event (contradiction).
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of concepts related to probability, specifically the concept of independent events and how to calculate the probability of combined events (contradiction).
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question requires students to apply their knowledge of probability to a scenario, demonstrating a higher-order thinking skill beyond simple recall.

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