If A speaks truth in 75% cases and B speaks truth in 80% cases, then the probability that they contradict each other in a statement, is:

\( \frac{7}{20} \)

The correct answer is Option (3) → \( \frac{7}{20} \)

Given:

Probability A speaks truth = $\frac{75}{100} = \frac{3}{4}$

Probability B speaks truth = $\frac{80}{100} = \frac{4}{5}$

They contradict each other if:

• A speaks truth and B lies
• A lies and B speaks truth

Probability A speaks truth and B lies = $\frac{3}{4} \cdot \left(1 - \frac{4}{5}\right) = \frac{3}{4} \cdot \frac{1}{5} = \frac{3}{20}$

Probability A lies and B speaks truth = $\left(1 - \frac{3}{4}\right) \cdot \frac{4}{5} = \frac{1}{4} \cdot \frac{4}{5} = \frac{4}{20}$

Total probability they contradict = $\frac{3}{20} + \frac{4}{20} = \frac{7}{20}$