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 (E/E1) Using Baye’s theorem P (E/E1) =