JEE Exam > JEE Questions > A man is known to speak truth 3 out of 4 time...
Start Learning for Free
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is
- a)1/2
- b)1/3
- c)3/8
- d)3/7
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A man is known to speak truth 3 out of 4 times. He throws a die and re...
Let E1, E2 and A be the events defined as follows
E1 = six occurs
E2= six does not occurs
A = the man reports that it is a six. We have.
E1 = six occurs
E2= six does not occurs
A = the man reports that it is a six. We have.
Now, P(A/E1)= Probability that the man reports that there is a six on the die given then 6 has occured on die
= Probability the man speaks truth
= Probability the man speaks truth
=3/4
P(A/E2) = Probability that the man reports that there is six is on die given that six has not occured on die
= Probability that the man does not speak truth
= Probability that the man does not speak truth
We have to find P(E1/A) i.e. the probability that there is six on the die given that the man has reported that there is six. By Baye's rule, we have
Free Test
FREE
| Start Free Test |
Community Answer
A man is known to speak truth 3 out of 4 times. He throws a die and re...
Problem:
A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is
a) 1/2
b) 1/3
c) 3/8
d) 3/7
Solution:
To solve this problem, we will use Bayes' theorem. Bayes' theorem is a fundamental concept in probability theory, which allows us to update our beliefs about an event based on new evidence.
Let's denote the event that the man speaks the truth as T, and the event that the die shows a six as D. We are given that P(T) = 3/4, which means that the probability of the man speaking the truth is 3/4. We want to find P(D|T), the probability that the die shows a six given that the man speaks the truth.
Applying Bayes' theorem:
Bayes' theorem states that:
P(D|T) = (P(T|D) * P(D)) / P(T)
Where:
P(D|T) is the probability of the die showing a six given that the man speaks the truth.
P(T|D) is the probability of the man speaking the truth given that the die shows a six.
P(D) is the probability of the die showing a six.
P(T) is the probability of the man speaking the truth.
Finding P(D|T):
We are given that the man speaks the truth 3 out of 4 times, so P(T|D) = 3/4.
The die has 6 faces, so the probability of rolling a six is 1/6, which gives us P(D) = 1/6.
Finding P(T):
We are given that P(T) = 3/4.
Calculating P(D|T):
Using Bayes' theorem:
P(D|T) = (P(T|D) * P(D)) / P(T)
P(D|T) = (3/4 * 1/6) / (3/4)
P(D|T) = 1/8 / 3/4
P(D|T) = 1/8 * 4/3
P(D|T) = 1/2 * 4/3
P(D|T) = 4/6
P(D|T) = 2/3
Therefore, the probability that the die is actually a six given that the man speaks the truth is 2/3.
The correct answer is option b) 1/3.
A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is
a) 1/2
b) 1/3
c) 3/8
d) 3/7
Solution:
To solve this problem, we will use Bayes' theorem. Bayes' theorem is a fundamental concept in probability theory, which allows us to update our beliefs about an event based on new evidence.
Let's denote the event that the man speaks the truth as T, and the event that the die shows a six as D. We are given that P(T) = 3/4, which means that the probability of the man speaking the truth is 3/4. We want to find P(D|T), the probability that the die shows a six given that the man speaks the truth.
Applying Bayes' theorem:
Bayes' theorem states that:
P(D|T) = (P(T|D) * P(D)) / P(T)
Where:
P(D|T) is the probability of the die showing a six given that the man speaks the truth.
P(T|D) is the probability of the man speaking the truth given that the die shows a six.
P(D) is the probability of the die showing a six.
P(T) is the probability of the man speaking the truth.
Finding P(D|T):
We are given that the man speaks the truth 3 out of 4 times, so P(T|D) = 3/4.
The die has 6 faces, so the probability of rolling a six is 1/6, which gives us P(D) = 1/6.
Finding P(T):
We are given that P(T) = 3/4.
Calculating P(D|T):
Using Bayes' theorem:
P(D|T) = (P(T|D) * P(D)) / P(T)
P(D|T) = (3/4 * 1/6) / (3/4)
P(D|T) = 1/8 / 3/4
P(D|T) = 1/8 * 4/3
P(D|T) = 1/2 * 4/3
P(D|T) = 4/6
P(D|T) = 2/3
Therefore, the probability that the die is actually a six given that the man speaks the truth is 2/3.
The correct answer is option b) 1/3.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer?
Question Description
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer?.
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer?.
Solutions for A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six isa)1/2b)1/3c)3/8d)3/7Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup