Question

If a tells truth 4 times out of 5 and b tells truth 3 times out of 4. the probability that both expressing the same fact contradict each other is:

Answer 1

Solution :-

Let A = The event that A speaks the truth

B = The event that B speaks the truth

Then,

P(A) = 4/5

P(B) = 3/4

Now,

A and B contradicts each other

= (A lies and B tells truth) or (A tells truth and B lies)

= P(A)*P(B - Lies) + P(A - Lies)*P(B)

= (4/5)*(1/4) + (1/5)*(3/4)

= 1/5 + 3/20

Taking L.C.M. of the denominators and then solving it.

= (4 + 3)/20

= 7/20

= (7*100)20

= 35 %

Answer.