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Question -

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4. What is the probability that the student knows the answer given that he answered it correctly?



Answer -

Let E1 bethe event that the student knows the answer, E2 be the eventthat the student guess the answer and A be the event that the answer iscorrect.

Then P (E1)= ¾

And P (E2)= ¼

Also P (A|E1)= P (correct answer given that he knows) = 1

And P (A|E2)= P (correct answer given that he guesses) = ¼

Now the probabilitythat he knows the answer, being given that answer is correct, is P (E1|A).

By using Bayes’theorem, we have:

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