Question

A speaks the truth 3 out' of 4 time, and b 5 out of 6 times . what is the probability that they will contradict each other in stating the same fact?

Answer 1

"Let A = Event that A speaks the truth

B = Event that B speaks the truth

Then P(A) =  3/4

P(B)  = 5/6

P(A-lie) = 1-3/4 = 1/4

P(B-lie) = 1-5/6 = 1/6

Now

A and B contradict each other =

[A lies and B true] or [B true and B lies]

= P(A).P(B-lie) + P(A-lie).P(B)

[Please note that we are adding at the place of OR]

= (3/4/*1/6) + (1/4*5/6) = 8/24

= (8/24 * 100) % = 33.33%

"