'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{13}{50}$
Let:
• Probability that A speaks the truth = $P(A_T) = \frac{4}{5}$
• Probability that A lies = $P(A_L) = \frac{1}{5}$
• Probability that B speaks the truth = $P(B_T) = \frac{9}{10}$
• Probability that B lies = $P(B_L) = \frac{1}{10}$
A and B contradict each other in two cases:
1. A tells truth and B lies: $P(A_T \cap B_L) = \frac{4}{5} \cdot \frac{1}{10} = \frac{4}{50}$
2. A lies and B tells truth: $P(A_L \cap B_T) = \frac{1}{5} \cdot \frac{9}{10} = \frac{9}{50}$
Total probability of contradiction = $\frac{4}{50} + \frac{9}{50} = \frac{13}{50}$