VITEEE 2017 Paper

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) =
=

xy.1

xy.1+(1−x)(1−y).1

=

xy

1−x−y+2xy