A speaks the truth in 70% of the cases and B speaks the truth in 80% of the cases, independently of each other. The probability that they contradict each other in stating the same fact is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.38
They contradict each other when one speaks the truth and the other does not. These two cases cannot happen together, so their probabilities are added. A and B are independent, so in each case the probabilities are multiplied.
\(P(\text{A true, B false}) = 0.7\times 0.2 = 0.14\)
\(P(\text{A false, B true}) = 0.3\times 0.8 = 0.24\)
Adding:
\(P(\text{contradict}) = 0.14+0.24 = 0.38\)
Why the other options are incorrect
Option (2) 0.62 — Incorrect. This is 1 − 0.38, the probability that they agree.
Option (3) 0.56 — Incorrect. This is \(0.7\times 0.8\), the probability that both speak the truth.
Option (4) 0.06 — Incorrect. This is \(0.3\times 0.2\), the probability that both are false.