Question

A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
1. 35%
2. 45%
3. 15%
4. 5%

Answer 1

Correct Answer - Option 1 : 35%

Given:

A speaks truth in 75% cases

B speaks truth in 80% cases

Calculation:

Let even that A speaks the truth be A

And even that B speaks the truth be B

According to the question:

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 [A true and B lies]

⇒ P(A) × P(B – lie) + P(A – lie) × P(B)

⇒ (3/4 × 1/5) +  (1/4 × 4/5)

⇒ 3/20 + 4/20 = 7/20 

Required percentage = 7/20 × 100 = 35%

∴ The Required percentage is 35%.