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
Let $T_1$ be the event that the first person speaks truth
$P(T_1)=0.6,\;P(T_1')=0.4$
Let $T_2$ be the event that the second person speaks truth
$P(T_2)=0.8,\;P(T_2')=0.2$
They agree if both speak truth or both lie
$P(\text{agreement})=P(T_1T_2)+P(T_1'T_2')$
$=P(T_1)P(T_2)+P(T_1')P(T_2')$
$=0.6\times0.8+0.4\times0.2$
$=0.48+0.08$
$=0.56$
The probability that both agree is $0.56$.