Question

The probability that A and B will tell the truth are 2/3 and 4/5 respectively.
What is the probability that
(1) They agree will each other?
2) They contradict each other while giving a testimony in the court.​

Answer 1

Answer: A) 3/5

Explanation:

Let A be the event of A will tell truth. B be the event of B tell truth

P(A)=2/3,P(Ac)=1−P(A)=1/3P(A)=2/3,P(Ac)= 1-P(A)=1/3

P(B)=4/5,P(Bc)=1−P(B)=1/5P(B)=4/5,P(Bc)=1-P(B)=1/5

When both agree then they say true or they say false together, that is

A∩B or Ac∩BcA∩B or Ac∩Bc

Also these events will be mutually exclusive :

P(A∩B)+P(Ac∩Bc)=P(A)P(B)P(C)=2/3*4/5+1/3*1/5=3/5P(A∩B)+P(Ac∩Bc)=P(A)P(B)P(C)=2/3*4/5+1/3*1/5=3/5

how u got the ans