Question

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. plz give explaination.

Answer 1

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) = 1−3/4= 1/4

P(B-lie) = 1−4/5= 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)

= (3/5*1/5)+(1/4*4/5)=7/20  

= (7/20*100)= or  35/100  or 35%  ANS