Question

The probability that A speaks is 4/5and probability for B is 3/4. the probability that they contradict each other when asked to speak on a fact is

7/20 . Aieee2004

Pls ans in detail ☺ pls put it on paper

Answer 1

Let A = Event that A speaks the truth
B = Event that B speaks the truth

Then P(A) = 4/5

P(B) = 3/4

P(A-lie) = 1-4/5 = 1/5

P(B-lie) = 1-3/4 = 1/4

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]

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

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