Question:

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

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Contradiction happens when one is truthful and the other lies. Multiply probabilities accordingly.
Updated On: Aug 7, 2025
  • 5%
  • 15%
  • 35%
  • 45%
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The Correct Option is C

Solution and Explanation

Let us denote: P(A tells truth) = 0.75 P(A lies) = 1 - 0.75 = 0.25
P(B tells truth) = 0.80
P(B lies) = 1 - 0.80 = 0.20 Contradiction occurs when one tells the truth and the other lies: \[ \text{Contradiction} = P(A \text{ true}) \cdot P(B \text{ false}) + P(A \text{ false}) \cdot P(B \text{ true})
= (0.75)(0.20) + (0.25)(0.80) = 0.15 + 0.20 = 0.35 \] \[ \Rightarrow \boxed{35%} \] \fbox{Final Answer: (C) 35%}
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