They contradict when one tells the truth and the other lies.

Let \( p_A = 0.6 \) (A tells truth) and \( p_B = 0.5 \) (B tells truth).

\[ P(\text{contradict}) \;=\; P(A\ \text{true},\,B\ \text{lie}) + P(A\ \text{lie},\,B\ \text{true}) \;=\; p_A(1-p_B) + (1-p_A)p_B. \]

\[ =\; 0.6(1-0.5) + (1-0.6)\cdot 0.5 \;=\; 0.6\cdot 0.5 + 0.4\cdot 0.5 \;=\; 0.30 + 0.20 \;=\; 0.50. \]

Answer: \(50\%\).