A and B arc 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 on a certain statement.
The probability that the statement is true is

A and B will agree on a certain statement if both speak truth or both lie. We define the following events:

 E₁= A and B both speak truth $\Rightarrow P\left(E_1\right)=xy$

E₂= A and B both lie $\Rightarrow P\left(E_2\right)=(1-x)(1-y)$

E = A and B agree on a certain statement 

Clearly, $\mathrm{P}\left(\mathrm{E}/{\mathrm{E}}_1\right)=1\text{ and }\mathrm{P}\left(\mathrm{E}/{\mathrm{E}}_2\right)=1$ The required probability is $\mathrm{P}\left({\mathrm{E}}_1/\mathrm{E}\right)$. 

Using Bayes' theorem

$\begin{array}{c}\mathrm{P}\left({\mathrm{E}}_1/\mathrm{E}\right)=\frac{\mathrm{P}\left({\mathrm{E}}_1\right)\mathrm{P}\left(\mathrm{E}/{\mathrm{E}}_1\right)}{\mathrm{P}\left({\mathrm{E}}_1\right)\mathrm{P}\left(\mathrm{E}/{\mathrm{E}}_1\right)+\mathrm{P}\left({\mathrm{E}}_2\right)\mathrm{P}\left(\mathrm{E}/{\mathrm{E}}_2\right)}\\ =\frac{\mathrm{xy}\times 1}{\mathrm{xy}\times 1+(1-\mathrm{x})(1-\mathrm{y})1}=\frac{\mathrm{xy}}{1-\mathrm{x}-\mathrm{y}+2\mathrm{xy}}\end{array}$