Question

'X' speaks true in 60% and 'y' in 50% of the cases. The probability that they contradict each other narrating the same incident is ........

Answer 1

Let A = Event that X speaks the truth
B = Event that Y speaks the truth

Then P(X) = 60/100 = 3/5
P(Y) = 50/100 = 1/2

P(X-lie) = 1-3/5 = 2/5
P(Y-lie) = 1-1/2 = 1/2

Now
X and Y contradict each other =
[X lies and Y true] or [Y true and Y lies]
= P(X).P(Y-lie) + P(X-lie).P(Y)
[Please note that we are adding at the place of OR]
= (3/5*1/2) + (2/5*1/2) = 5/10
= 1/2