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C
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Difficulty:
95%
(hard)
Question Stats:
25% (02:14) correct
75%
(02:09)
wrong
based on 101
sessions
History
Date
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Not Attempted Yet
In an examination comprising 20 questions, each question has five answer choices, of which only one is correct. The probability of a candidate knowing the answer to any question is 4/5. The candidate makes a random guess, if he does not know the answer to a question. What is the probability of the candidate not knowing the answer to the first question, if it is known that the answer marked by the candidate to that question was correct?
A. 1/25
B. 1/5
C. 1/21
D. 4/25
E. 6/25
A. 1/25
B. 1/5
C. 1/21
D. 4/25
E. 6/25
26 Jul 2012, 08:19
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Smita04
In an examination comprising 20 questions, each question has five answer choices, of which only one is correct. The probability of a candidate knowing the answer to any question is 4/5. The candidate makes a random guess, if he does not know the answer to a question. What is the probability of the candidate not knowing the answer to the first question, if it is known that the answer marked by the candidate to that question was correct?
A. 1/25
B. 1/5
C. 1/21
D. 4/25
E. 6/25
I don't have the OA.
A. 1/25
B. 1/5
C. 1/21
D. 4/25
E. 6/25
I don't have the OA.
We are given that the candidate answered the first question correctly and we are asked to find the probability that the candidate didn't know the answer to this question.
What is the probability that the candidate answers the question correctly:
If the candidate knows the answer, then the probability is \(\frac{4}{5}*1=\frac{20}{25}\);
If the candidate does NOT know the answer, then the probability is \(\frac{1}{5}*\frac{1}{5}=\frac{1}{25}\);
So, in 20+1=21 cases out of 25 the candidate answers the first question correctly. Out of those 21 cases in 1 case the candidate does NOT know the answer, hence the probability that the candidate answered the first question correctly but didn't know the answer to this question is \(\frac{1}{21}\).
Answer: C.
P.S. Not a GMAT question.
General Discussion
21 Jan 2025, 03:03
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In an examination comprising 20 questions, each question has five answer choices, of which only one is correct. The probability of a candidate knowing the answer to any question is 4/5. The candidate makes a random guess, if he does not know the answer to a question.
What is the probability of the candidate not knowing the answer to the first question, if it is known that the answer marked by the candidate to that question was correct?
The probability that the candidate knows the answer marked it correctly = (4/5*1 = 4/5 = 20/25
The probability that the candidate does not know the answer to the question and marked it correcly= (1/5)*(1/5) = 1/25
In Toal 21 cases of marking the answer correctly, the probability of the candidate not knowing the answer to the question = 1/21
IMO C
What is the probability of the candidate not knowing the answer to the first question, if it is known that the answer marked by the candidate to that question was correct?
The probability that the candidate knows the answer marked it correctly = (4/5*1 = 4/5 = 20/25
The probability that the candidate does not know the answer to the question and marked it correcly= (1/5)*(1/5) = 1/25
In Toal 21 cases of marking the answer correctly, the probability of the candidate not knowing the answer to the question = 1/21
IMO C
