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

A 30/100

B 35/100

C 45/100

D 50/100

Correct Answer: Option B

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) = \(1-\frac34\) = 1/4

P(B-lie) = \(1-\frac45\) = 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)

= \(\left(\frac35\times\frac15\right)+\left(\frac14\times\frac45\right)=\frac7{20}\)

= \(\left(\frac7{20}\times100\right)\)

= 35%