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

Answers (1)


A : Student knows answer.

B : Student guess the answer

C : Answer is correct 

P(A)=\frac{3}{4}         P(B)=\frac{1}{4}



By Bayes theorem :


                 P(A|C)=\frac{\frac{3}{4}\times 1}{\frac{3}{4}\times 1+\frac{1}{4}\times \frac{1}{4}}

                  =\frac{\frac{3}{4}}{\frac{3}{4}+\frac{1}{16}}     =\frac{\frac{3}{4}}{\frac{13}{16}}


Posted by

seema garhwal

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