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There are 2 cases in which they would contradict each other. 1.) A tells the truth and B lies .. the probability of this happening is 0.75*0.2 = 0.15

2.) A lies and B tells the truth .. the probability of which is 0.25 * 0.8 =0.2

So the answer is 0.15+0.2 = 0.35

Thanks a lot gabriel. the question is from LearnHub GMAT Community.

gabriel wrote:There are 2 cases in which they would contradict each other. 1.) A tells the truth and B lies .. the probability of this happening is 0.75*0.2 = 0.15

2.) A lies and B tells the truth .. the probability of which is 0.25 * 0.8 =0.2

So the answer is 0.15+0.2 = 0.35

Hi Gabriel,

I might be over thinking here but isn't assuming both A and B will lie in the same manner an incorrect assumption?

But what surprised me even more is my approach got me the same answer. My approach;

Assuming A and B to be two unfair coins and (T)ruth and (L)ie the two sides;

P(Not getting TT) = {P(AT) x P(BL)} + {P(AL) x P(BT)} + {P(AL) x P(BL)} = 3/20 + 3/20 + 1/20 = 35%

They would contradict when one speaks the truth and the other lies.

Case 1) A speaks truth and B lies

(3/4) * (1/5) = 3/20

Case 2) B speaks truth and A lies

(4/5) * (1/4) = 4/20

Total = Case 1 + Case 2 = 7/20 = 35%