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

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  1. Class 12
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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 𝟏𝟐﷮𝟏𝟑﷯

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