A speaks truth in $75\%$  of the cases and B in $80\%$  cases. What is the probability that their statements about an incident do not match. 

Probability of A speaks truth  $=P\left(A\right)=\frac{75}{100}$

$\mathrm{P}\left(\mathrm{A}\text{ tells lies }\right)=P\left(\overline{A}\right)=\frac{25}{100}$

$\mathrm{P}\left(\mathrm{B}\text{ tells truth }\right)=P\left(B\right)=\frac{80}{100}$

$P\left(\overline{B}\right)=P\left(\text{ B telling lies }\right)=\frac{20}{100}$

Probability of$A \& B$  statements do not match

$=P\left(A\right)P\left(\overline{B}\right)+P\left(\overline{A}\right)P\left(B\right)=\frac{75}{100}\cdot \frac{20}{100}+\frac{25}{100}\cdot \frac{80}{100}$

$=\frac{150}{100\times 10}+\frac{200}{100\times 10}=\frac{35}{100}=35\mathrm{\%}$