Question

A speaks truth in $75\%$ of the cases and B in $80\%$ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

Answer 1

Let $A=$ event where $A$ speaks the truth.

$B=$ event where $B$ speaks the truth.

$P\left(A\right)=75$%$=0.75$

$P\left(B\right)=80$%$=0.80$

$P\left(A^{\prime }\right)=0.25$

$P\left(B^{\prime }\right)=0.20$

where, $A^{\prime }$ and $B^{\prime }$ are events when they lie.

For them to contradict each other, one has to lie and the other has to be truthful.

$=\left(0.75\right)\left(0.2\right)+\left(0.8\right)\left(0.25\right)$

$=0.35=35$%