Question

The odds against A speaking the truth are 4:6 while the odds in favor of B speaking the truth are 7:3. What is the probability that
(a) a statement is true, if A and B agree on the statement?
(b) A and B contradict each other in stating the same fact?​

Answer 1

A : 3 :2 means that in 5 situation, A told the True 3 times; as a fraction 3/5; and A told the lies in ( 5 - 3)/ 5 = 2/5,

B : 7 : 3 means that 7 +3 = 10 situation, B told the True; in 7 out of 10. As a fraction 7/10 and B told lies in 3 out of 10 situations. As a fraction 3/10

Both contradict each other when A told the True and B lied. As fractions . . . . . . 3/5 x 3/10 = 9/ 50 = 18 %

Or A lied and B told the True. As fractions: 2/5 x 7/10 = 14/50 = 28 %

Both Agree. when A and B told the True; 3/5 x 7/10 = 21/50 or 42%

Both disagree when both lied; 2/5 x 3/5 = 6/50 = 12 %

Probability of Agreement : 42 + 12 = 54 %

Probability of Contradiction : 18 + 28 = 46 %: