Question

A person \(P\) speaks truth in \(75\%\) cases and another person \(R\) in \(80\%\) cases. Then the probability that they are likely to contradict each other in narrating the same event is

• A. \(\frac{7}{20}\)
• B. \(\frac{7}{10}\)
• C. \(0.2\)
• D. \(0.3\)

Hint:

When two people may tell truth or lie independently, contradiction occurs when exactly one tells the truth and the other lies.

Answer 1

The Correct Option is A

Step 1: Identify contradiction scenarios.
They contradict when exactly one tells the truth: (P truth, R lie) or (P lie, R truth).

Step 2: Compute.
\[P = \frac{3}{4}\cdot\frac{1}{5} + \frac{1}{4}\cdot\frac{4}{5} = \frac{3}{20}+\frac{4}{20} = \frac{7}{20}.\]
\[\boxed{\frac{7}{20}}\]