In a village, man speaks truth in 70% and women in 60% cases. If they were asked a question, what is the probability that they contradict each other?

Question : In a village, man speaks truth in 70% and women in 60% cases. If they are asked a question, what is the probability that they contradict each other?

Answer :

In a village, man speaks truth in 70% and women in 60% cases.

So their probabilities of speaking truth and false are

P(man speaks truth)=70% =0.7,

P(man speaks false)=100%-70% =30%=0.3,

P(women speaks truth)=60% =0.6,

and P(women speaks false)=100%-60% =40%=0.4

If they are asked a question then they contradict each other in the following two ways

(i) Man speaks truth and women speaks false

(ii) Man speaks false and women speaks true

Therefore the probability that they contradict each other on answering the question is calculated as

P{(Man speaks truth and women speaks false)}+P{(Man speaks false and women speaks truth)}

=0.7*0.4+0.3*0.6

=0.28+0.18

=0.46

Thus 0.46 is the probability that they will contradict each other on answering the question.