Question

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

Answer 1

A = A speak truth

B = Bspeak truth

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

P(A) x P(B-lie) + P(B) x P(A-lie)

3/4 x 1/6    +     5/6 x 1/4

= 3/24   +   5/24  

= 8/24 = 1/3

1/3   x 100 = 100/3 = 33.33%