ProbabilityMCQPYQ Nov. 20Question 3324 of 187
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If A\displaystyle A speaks 75%\displaystyle 75\% of truth and B\displaystyle B speaks 60%\displaystyle 60\% of truth. In what percentage both of them likely contradict with each other in narrating the same questions?

Options

A0.60\displaystyle 0.60
B0.45\displaystyle 0.45
C0.65\displaystyle 0.65
D0.35\displaystyle 0.35
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Correct Answer

✅ Option b — 0.45\displaystyle 0.45

All Options:

  • A0.60\displaystyle 0.60
  • B0.45\displaystyle 0.45
  • C0.65\displaystyle 0.65
  • D0.35\displaystyle 0.35

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Detailed Solution & Explanation

**Probability of Contradiction Between A and B** Given: - P(A speaks truth)=0.75\displaystyle P(A \text{ speaks truth}) = 0.75, so P(A lies)=0.25\displaystyle P(A \text{ lies}) = 0.25 - P(B speaks truth)=0.60\displaystyle P(B \text{ speaks truth}) = 0.60, so P(B lies)=0.40\displaystyle P(B \text{ lies}) = 0.40 They contradict each other when: 1. A speaks truth AND B lies: 0.75×0.40=0.30\displaystyle 0.75 \times 0.40 = 0.30 2. A lies AND B speaks truth: 0.25×0.60=0.15\displaystyle 0.25 \times 0.60 = 0.15 P(contradiction)=0.30+0.15=0.45P(\text{contradiction}) = 0.30 + 0.15 = 0.45 Note: The calculated answer is 0.45 (Option B), but given answer key is D = 0.35. By mathematical derivation the answer is **0.45**. Hence, **Option B** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

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Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

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