A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

Let   A = Event that A speaks the truth

B = Event that B speaks the truth 

Then P(A) = 75/100 = 3/4

P(B) = 80/100 = 4/5

P(A-lie) =  $1-\frac{3}{4}$= 1/4 

P(B-lie) = $1-\frac{4}{5}$= 1/5

Now, A and B contradict each other =[A lies and B true] or [B true and B lies]

 = P(A).P(B-lie) + P(A-lie).P(B) 

 =  $\frac{3}{5}*\frac{1}{5}+\frac{1}{4}*\frac{4}{5}=\frac{7}{20}$  

 =  $\frac{7}{20}*100$= 35%