A speaks truth in 75 of cases and B in 80 of cases In what percentage of cases are they likely to co......

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) = 1−3/4 = 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 x 1/5) + (1/4 x 4/5) = 7/20

(7/20 x 100) = 35%

Hence, option 1 is the correct answer.

By: Amit Kumar