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) $\frac{4}{5}$
Prev Next

AI Tutor Explanation

Powered by Gemini

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

AI Suggestion: Option A

AI generated content. Review strictly for academic accuracy.

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.

More from this Chapter

MCQ_SINGLE
Let E be an event of a sample space S of an experiment, then \(P(S|E)=\)
MCQ_SINGLE
If \(P(A)=\frac{1}{7}\), \(P(B)=\frac{5}{7}\) and \(P(A\cap B)=\frac{4}{7},\) then \(P(\overline{A}|B)\) is:
SUBJECTIVE
A person buys a smartphone from this shop. (i) Find the probability that it was defective. (ii) What is the probability that this defective smartphone was manufactured by company B ?
SA
There are two coins. One of them is a biased coin such that P (head): P (tail) is 1:3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
MCQ_SINGLE
Let E and F be two events such that \(P(E)=0\cdot1\), \(P(F)=0\cdot3,\) \(P(E\cup F)=0\cdot4\) then \(P(F|E)\) is:
View All Questions