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:
Answer & explanation
Correct answer: option 3
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 = $\frac{3}{20} + \frac{4}{20} = \frac{7}{20}$