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

A. 35%

B. 5%

C. 45%

D. 22.5%

Solution:

Different possible cases of contradiction,
A speaks truth and B does not speaks truth.
Or, A does not speak truth and B speaks truth.

\begin{aligned} = (\frac{3}{4} \times \frac{1}{5}) + (\frac{1}{4} \times \frac{4}{5}) \\ = \frac{3}{20} + \frac{4}{20} \\ = \frac{7}{20} \\ = 35 % \end{aligned}

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