'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

$\frac{13}{50}$

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 = $\frac{4}{50} + \frac{9}{50} = \frac{13}{50}$