A and B will agree on a certain statement if both speak the truth or both tell a lie. Now, let us define the events as follows:

E_{1}: A and B both speak the truth ⇒** P(E1) = xy **

E_{2}: A and B both tell a lie ⇒ **P(E**_{2}) = (1 – x) (1 – y)

E: A and B agree on a certain statement.

Clearly, **P(E/E**_{1}) = P(E/E_{2}) = 1

Now, we are required to find P(E_{1}/E).

P(E_{1}/E) = \(\frac{P(E_1).P(E/E_1)}{P(E_1).P(E/E_1)+P(E_2).P(E/E_2)}\) = \(\frac{xy.1}{xy.1+(1-x)(1-y).1}\) = **\(\frac{xy}{1-x-y+2xy}\)**