Ex 13.3, 4 - In answering a question on multiple choice test - Ex 13.3

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  1. Chapter 13 Class 12 Probability
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Ex 13.3, 4 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? Let A : student know the answer B : student guesses C : student answers correctly We need to find the Probability that the student knows the answer, if he answered it correctly i.e. P(A|C) P(A|C) = P(A) . P(C|A) P(B) . P(C|B) + P(A) P(C|A) Putting values in formula, P(A|C) = 3 4 1 1 4 1 4 + 1 4 1 = 1 4 3 1 4 1 4 +3 = 3 1 4 + 3 = 3 13 4 = 12 13 Therefore, required probability is

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