GATE Exam > GATE Questions > The probability that a student knows the corr...
Start Learning for Free
The probability that a student knows the correct answer to a multiple choice question is 2/3 . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student known the correct answer is
- a)2/3
- b)3/4
- c)5/6
- d)8/9
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The probability that a student knows the correct answer to a multiple ...
Most Upvoted Answer
The probability that a student knows the correct answer to a multiple ...
Given:
The probability that a student knows the correct answer to a multiple-choice question is 2/3.
If the student does not know the answer, then the student guesses the answer.
The probability of the guessed answer being correct is 1/4.
To find:
Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer.
Solution:
Let's denote the events as follows:
A: The student knows the correct answer.
B: The student answers the question correctly.
We are given that the probability of A is 2/3. Therefore, the probability of not A (i.e., the student does not know the answer) is 1 - 2/3 = 1/3.
We are also given that if the student does not know the answer, the probability of guessing it correctly is 1/4. Therefore, the probability of B given not A is 1/4.
Using Bayes' theorem, we can find the conditional probability of A given B:
P(A|B) = (P(B|A) * P(A)) / P(B)
Calculating P(B):
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= (1 * 2/3) + (1/4 * 1/3)
= 2/3 + 1/12
= 8/12 + 1/12
= 9/12
= 3/4
Calculating P(A|B):
P(A|B) = (P(B|A) * P(A)) / P(B)
= (1 * 2/3) / (3/4)
= 2/3 * 4/3
= 8/9
Thus, the conditional probability that the student knows the correct answer, given that the student has answered the question correctly, is 8/9.
Therefore, the correct answer is option D) 8/9.
The probability that a student knows the correct answer to a multiple-choice question is 2/3.
If the student does not know the answer, then the student guesses the answer.
The probability of the guessed answer being correct is 1/4.
To find:
Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer.
Solution:
Let's denote the events as follows:
A: The student knows the correct answer.
B: The student answers the question correctly.
We are given that the probability of A is 2/3. Therefore, the probability of not A (i.e., the student does not know the answer) is 1 - 2/3 = 1/3.
We are also given that if the student does not know the answer, the probability of guessing it correctly is 1/4. Therefore, the probability of B given not A is 1/4.
Using Bayes' theorem, we can find the conditional probability of A given B:
P(A|B) = (P(B|A) * P(A)) / P(B)
Calculating P(B):
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= (1 * 2/3) + (1/4 * 1/3)
= 2/3 + 1/12
= 8/12 + 1/12
= 9/12
= 3/4
Calculating P(A|B):
P(A|B) = (P(B|A) * P(A)) / P(B)
= (1 * 2/3) / (3/4)
= 2/3 * 4/3
= 8/9
Thus, the conditional probability that the student knows the correct answer, given that the student has answered the question correctly, is 8/9.
Therefore, the correct answer is option D) 8/9.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer?
Question Description
The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer?.
The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer?.
Solutions for The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probability that a student knows the correct answer to a multiple choicequestion is2/3. If the student does not know the answer, then the studentguesses the answer. The probability of the guessed answer being correct is1/4. Given that the student has answered the question correctly, the conditionalprobability that the student known the correct answer isa)2/3b)3/4c)5/6d)8/9Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
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