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

Answer 1

Correct option (d)

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) = 1

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