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?.
Last updated date: 23rd Mar 2023
•
Total views: 303.9k
•
Views today: 7.82k
Answer
303.9k+ views
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 person’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 Sheela’s not speaking the truth is (100-35) % = 65% or (1-.35) = 0.65
which is represented as P(S′) =0.65
If Ramesh does not tell truth means he is lying so probability of Ramesh’s not speaking the truth is (100-75) % = 25% or (1-.75) = 0.25
which is represented as P(R′) = 0.25
where, A′ and B′ are events when they lie.
For them to contradict each other, one has to lie and the other has to be truthful.
= P(S)×P(R′) + P(S′) × P(R)
= (0.35) × (0.25) +(0.65) × (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.
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 person’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 Sheela’s not speaking the truth is (100-35) % = 65% or (1-.35) = 0.65
which is represented as P(S′) =0.65
If Ramesh does not tell truth means he is lying so probability of Ramesh’s not speaking the truth is (100-75) % = 25% or (1-.75) = 0.25
which is represented as P(R′) = 0.25
where, A′ and B′ are events when they lie.
For them to contradict each other, one has to lie and the other has to be truthful.
= P(S)×P(R′) + P(S′) × P(R)
= (0.35) × (0.25) +(0.65) × (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.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
