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) → \(\displaystyle\frac{7}{20}\)
Let \(P(A) = \frac{3}{4}\) and \(P(B) = \frac{4}{5}\) be the probabilities that A and B speak the truth. They contradict each other when exactly one of them speaks the truth. Taking A and B as independent:
\(\displaystyle P = \frac{3}{4}\cdot\frac{1}{5} + \frac{1}{4}\cdot\frac{4}{5}\)
\(\displaystyle = \frac{3}{20} + \frac{4}{20} = \frac{7}{20}\)