Question

Chance that Sheela tells the truth is 35% and for Ramesh it is 75%. In what percentage they are likely to contradict each other in stating the same fact?.

Hint: In order to solve this problem, we must know the total probability of any event equal to 1 along with proper understanding of the condition of Contradiction.

Complete Step-by-Step Solution:

Let S= event where Sheela speaks the truth.
R= event where Ramesh speaks the truth.

In question it is given
Sheela tells truth is 35%, probability of Sheela speaks the truth is .35
It is represented as P(S) =35%=0.35

Ramesh tells truth is 75%, probability of Ramesh speaks the truth is .75
It is represented as P(R) =75%=0.75

We know that the total probability of any event is equal to 1. For example, a person can speak either truth or false, not both at a time. Hence the total probability of a personâ€™s speaking (true or false) will be 1.
And probability of lying = 1 - Probability of speaking truth.

If Sheela does not tell truth means she is lying so probability of Sheelaâ€™s not speaking the truth is (100-35) % = 65% or (1-.35) = 0.65
which is represented as P(Sâ€²) =0.65
If Ramesh does not tell truth means he is lying so probability of Rameshâ€™s not speaking the truth is (100-75) % = 25% or (1-.75) = 0.25
which is represented as P(Râ€²) = 0.25
where, Aâ€² and Bâ€² are events when they lie.
For them to contradict each other, one has to lie and the other has to be truthful.
= P(S)Ã—P(Râ€²) + P(Sâ€²) Ã— P(R)
= (0.35) Ã— (0.25) +(0.65) Ã— (0.75)
=0.575=57.5%
Note- Whenever we face such types of problems the key concept we have to remember is that we always remember the total probability of any event equal to 1, And how to find the probability of lying which is stated above. So with the help of these concepts we will get our required probability.