Question

$A$ speaks truth in $75\%$ of the cases and $B$ in $80\%$ of the cases. The percentage of cases they are likely to contradict each other in making the same statement is

• A. $20\%$
• B. $35\%$
• C. $45\%$
• D. $65\%$

Answer 1

The correct option is B $35\%$

For contradictory statement : either $A$ speaks truth and $B$ speaks false or vice-versa
So, Required probability
$=P(A\cap B^c)\cup P(A^c\cap B)=P\left(A\right)\cdot P\left(B^c\right)+P\left(A^c\right)\cdot P\left(B\right)$
[As, both events are independent]
$=\frac{75}{100}\cdot \frac{20}{100}+\frac{25}{100}\cdot \frac{80}{100}=\frac{7}{20}=35\%$