Question

A speak truth in 75% of cases and B in 80% of cases . the percentage of cases they are likely to contradict each other in stating the same fact, is (give me full answer)
(a) 30%
(b) 35%
(c) 45%
(d) 25%

Answer 1

Answer: Option B

Explanation:

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)

[Please note that we are adding at the place of OR]

= (3/5*1/5) + (1/4*4/5) = 7/20

= (7/20 * 100) % = 35%