A speaks truth in 75% of the cases, while B speaks truth in 90% of the cases. What is the probability that A and B contradict each other?

Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then,
P(A) = 75/100 = 3/4
P(B) = 90/100 = 9/10
P(A - lie) = 1 - P(A) = 1 - 3/4 = 1/4
P(B - lie) = 1 - P(B) = 1 - 9/10 = 1/10
Now, A and B contradict each other = [A lies and B true] or [B lies and A true]
= P(A lies) * P(B true) + P(B lies) * P(A true)
= P(A - lie) * P(B) + P(B - lie) * P(A)
= (1/4) * (9/10) + (1/10) * (3/4)
= 9/40 + 3/40
= 12/40
= 3/10
= 3/10 * 100 = 30%