‘A’ speaks truth in 75% of the cases and B in 80% of the cases then the probability for

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Both speak truth is $\frac{3}{5}$

Both speak lie is $\frac{1}{20}$

Their statements about an incident do not match is $\frac{7}{20}$

The statements about an incident are coincides is $\frac{13}{20}$

answer is A, B, C, D.

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Detailed Solution

$\begin{array}{l} P (A) = 75 % \Rightarrow P (A) = \frac{75}{100}; P (\bar{A}) = \frac{25}{100} \\ P (B) = 80 % \Rightarrow P (B) = \frac{80}{100}; P (\bar{B}) = \frac{20}{100} \\ (A) P (A \cap B) = P (A) . P (B) = \frac{3}{4} . \frac{4}{5} = \frac{3}{5} \\ (B) P (\bar{A} \cap \bar{B}) = P (\bar{A}) . P (\bar{B}) = \frac{3}{4} \times \frac{4}{5} = \frac{3}{5} \\ (C) \frac{3}{4} . \frac{1}{5} + \frac{1}{4} . \frac{4}{5} \Rightarrow \frac{7}{20} \\ (D) \frac{3}{4} . \frac{4}{5} + \frac{1}{4} . \frac{1}{5} = \frac{13}{20} \end{array}$