CUET · MATHS · PYQ PAPER 2025
One person speaks truth in \(60 \%\) of the cases and another person in \(80 \%\) of the cases. They are likely to agree in stating the same fact in:
- A \(48 \%\) of the cases
- B \(56\%\) of the cases
- C \(58 \%\) of the cases
- D \(70 \%\) of the cases
Answer & Solution
Correct Answer
(B) \(56\%\) of the cases
Step-by-step Solution
Detailed explanation
\( P(\text{agree}) = P(\text{truth}_1)P(\text{truth}_2) + P(\text{lie}_1)P(\text{lie}_2) \) \( P(\text{agree}) = (0.6)(0.8) + (1-0.6)(1-0.8) \) \( P(\text{agree}) = 0.48 + (0.4)(0.2) \) \( P(\text{agree}) = 0.48 + 0.08 \) \( P(\text{agree}) = 0.56 = 56 \\% \)
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