One person speaks truth in 60% of the cases and another person in 80% of the cases. They are likely to agree in stating the same fact in
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 56% of the cases
The two persons speak independently. They agree in stating the same fact when both speak the truth or both lie.
\(P(\text{both truthful}) = 0.6 \times 0.8 = 0.48\)
\(P(\text{both lie}) = 0.4 \times 0.2 = 0.08\)
\(P(\text{agree}) = 0.48 + 0.08 = 0.56\)
So they agree in 56% of the cases.
Why the other options are incorrect
Option (1) 48% of the cases — Incorrect. This counts only the cases where both speak the truth; when both lie they also state the same fact.
Option (3) 58% of the cases — Incorrect. It does not equal 0.48 + 0.08.
Option (4) 70% of the cases — Incorrect. This is the average of 60% and 80%, not the probability that they agree.