Question

A and B are two independent witnesses (i.e. there is no collusion between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. The probability that the statement is true is

(a) x -y/x + y

(b) xy/1 + x + y + xy

(c) x-y/1 - x - y + 2xy

(d) xy/1 - x - y + 2xy

Answer 1

Correct option (d) xy/1 - x - y + 2xy

Explanation:

A and B will agree in a certain statement if both speak truth or both tell a lie. We define following events

E1 = A and B both speak truth

P(E1) = xy

E2 = A and B both tell a lie

P (E2) = (1 – x ) (1 – y)

E = A and B agree in a certain statement

Clearly, P(E/ E1) = 1 and P(E / E2) 2 = 1

The required probability is P(E1 / E) . Using Baye’* theorem