ProbabilityMCQMTP June 24 Series IQuestion 2833 of 295
All Questions

A speaks truth in 75%\displaystyle 75\% cases and B in 60%\displaystyle 60\% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident.

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

Let TA\displaystyle T_A be the event that A speaks the truth, and TB\displaystyle T_B be the event that B speaks the truth. We are given: - P(TA)=75%=0.75  ⟹  P(TA′)=1−0.75=0.25\displaystyle P(T_A) = 75\% = 0.75 \implies P(T_A') = 1 - 0.75 = 0.25 - P(TB)=60%=0.60  ⟹  P(TB′)=1−0.60=0.40\displaystyle P(T_B) = 60\% = 0.60 \implies P(T_B') = 1 - 0.60 = 0.40 A and B contradict each other when one of them speaks the truth and the other lies. Assuming their actions are independent: P(contradict)=P(TA)P(TB′)+P(TA′)P(TB)\displaystyle P(\text{contradict}) = P(T_A)P(T_B') + P(T_A')P(T_B). Substitute the values: P(contradict)=(0.75×0.40)+(0.25×0.60)=0.30+0.15=0.45\displaystyle P(\text{contradict}) = (0.75 \times 0.40) + (0.25 \times 0.60) = 0.30 + 0.15 = 0.45. Converting to percentage: Percentage of cases=0.45×100%=45%\displaystyle \text{Percentage of cases} = 0.45 \times 100\% = 45\%. In decimal representation, this is 0.45\displaystyle 0.45, which corresponds to Option B. 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.

View Official ICAI Syllabus

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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