'X' speaks truth in 60% and 'Y' in 50% of the cases. The probability that they contradict each other while narrating the some incident, is
Answer & explanation
Correct answer: option 3
Consider the following events:
A='X' speaks truth, B='Y' speaks truth.
Then, $P(A) =\frac{60}{100}=\frac{3}{5}$ and $ P(B) = \frac{50}{100}=\frac{1}{2}$
Required probability $=((A ∪ \overline{B}) ∪ (\overline{A} ∩ B))$
$=(A ∩ \overline{B}) +P (\overline{A} ∩ B)$
$=\frac{3}{5}×\frac{1}{2}+\frac{2}{5}×\frac{1}{2}= \frac{1}{2}$