The probability that A speaks truth is $\frac{4}{5}$, while this probability for B is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is

$\frac{7}{20}$

Consider the following events:

E = A speaks truth, F= B speaks truth.

We have, $P(E)=\frac{4}{5}$ and $P(F)=\frac{3}{4}$

Required probability $= P((E ∩ \overline{F})∪ (\overline{E} ∩ F))$

$= P(E ∩ \overline{F})+P(\overline{E} ∩ F)$

$=P(E) P(F)+P(F)+P(\overline{E}) P(F)$

$= \frac{4}{5}× \left(1-\frac{3}{4}\right) +\left(1-\frac{4}{5}\right)× \frac{3}{4}=\frac{7}{20}$