A speaks truth in 80% cases and B in 90% cases. The probability that they contradict each other in stating the same fact, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{13}{50} \)
Let A and B also denote the events that A and B speak the truth. They speak independently.
\( \displaystyle P(A)=0.8,\ P(A')=0.2 \)
\( \displaystyle P(B)=0.9,\ P(B')=0.1 \)
They contradict each other when exactly one of them speaks the truth:
\( \displaystyle P=P(A)P(B')+P(A')P(B) \)
\( \displaystyle =0.8\times 0.1+0.2\times 0.9 \)
\( \displaystyle =0.08+0.18=0.26 \)
\( \displaystyle =\frac{13}{50} \)