A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:

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: \[ P(\text{Contradiction}) = 0.2 + 0.3 = \boxed{0.5} \]

✅ Final Answer:

\[ \boxed{\frac{1}{2}} \]