If a person A speaks the truth in 80% cases and the person B speaks the truth in 75% cases, then the probability that they contradict each other in a statement is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{7}{20}$
Let A speaks truth with probability $0.8$ and lies with $0.2$.
B speaks truth with probability $0.75$ and lies with $0.25$.
They contradict each other when:
(truth by A, lie by B) OR (lie by A, truth by B)
$P = 0.8 \cdot 0.25 + 0.2 \cdot 0.75$
$P = 0.20 + 0.15$
$P = 0.35$
$0.35$