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In answering a question on a MCQ test with 4 choices per question, a student knows the answer, guesses or copies the answer. Let ½ be the probability that he knows the answer, ¼ be the probability that he guesses and ¼ that he copies it. Assuming that a student, who copies the answer, will be correct with the probability ¾, what is the probability that the student knows the answer, given that he answered it correctly?
  • a)
     0.5  
  • b)
     0.8  
  • c)
     0.7  
  • d)
     None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In answering a question on a MCQ test with 4 choices per question, a s...
To solve this problem, we can use Bayes' theorem. Bayes' theorem is a mathematical formula that helps us calculate conditional probabilities. In this case, we want to find the probability that the student knows the answer given that he answered it correctly.

Let's define the events:
- K: The student knows the answer
- G: The student guesses the answer
- C: The student copies the answer
- A: The student answers the question correctly

We are given the following probabilities:
- P(K) =
- P(G) =
- P(C) =
- P(A|K) = 1 (since if the student knows the answer, he will answer correctly)
- P(A|G) = 1/4 (since there are 4 choices and the student is guessing)
- P(A|C) = (the probability that the student copies the answer correctly)

We want to find P(K|A), the probability that the student knows the answer given that he answered correctly.

Applying Bayes' theorem, we have:

P(K|A) =

To calculate P(A), we can use the law of total probability:

P(A) = P(A|K)P(K) + P(A|G)P(G) + P(A|C)P(C)

P(A) = 1 * + 1/4 * + *

Now let's substitute the values:

P(A) =

Now we can calculate P(K|A):

P(K|A) =

Simplifying the expression:

P(K|A) =

P(K|A) =

Therefore, the probability that the student knows the answer, given that he answered it correctly, is option D (none of these).

Note: The question does not provide the value of (the probability that the student copies the answer correctly), so we cannot determine the exact value of P(K|A).
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In answering a question on a MCQ test with 4 choices per question, a student knows the answer, guesses or copies the answer. Let be the probability that he knows the answer, be the probability that he guesses and that he copies it. Assuming that a student, who copies the answer, will be correct with the probability , what is the probability that the student knows the answer, given that he answered it correctly?a)0.5 b)0.8 c)0.7 d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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