Q. 374.8( 4 Votes )

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 a student knows the answer given that he answered it correctly?

Answer :

Let us assume U1, U2, and A be the events as follows:


U1 = Knowing the answer


U2 = Guessing the answer


A = Answering the question correctly


From the problem




P(A|U1) = P(Answering the question correctly by knowing the answer)


P(A│U1 ) = 1


P(A|U2) = P(Answering the question correctly by guessing the answer)



Now we find


P(U1|A) = P(The answer is known given that he answerd the question correctly)


Using Baye’s theorem:







The required probability is.


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