A speaks the truth in 40% of the cases and B in 50% of the cases.

What is the probability that they contradict each other while narrating an incident?

? Let’s Define:

• $P(A_T) = 0.4$ → A tells the truth
• $P(A_L) = 0.6$ → A lies
• $P(B_T) = 0.5$ → B tells the truth
• $P(B_L) = 0.5$ → B lies

? Contradiction happens in two cases:

• A tells the truth, B lies → $0.4 \times 0.5 = 0.2$
• A lies, B tells the truth → $0.6 \times 0.5 = 0.3$

Total probability of contradiction:

✅ Final Answer: