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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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(A) . P(C|A) + P(B) P(C|B) " "P(A)" = Probability that student knows the answer = 𝟑/𝟒 "P(C|A)" = Probability that the student correctly, if he knows the answer = 1 "P(B)" = Probability that the student guesses the answer = 𝟏/𝟒 "P(C|B)" = Probability that the student correctly, if he guesses = 𝟏/𝟒 Putting values in formula, P(A|C) = (𝟑/𝟒 × 𝟏)/( 𝟏/𝟒 × 𝟏/𝟒 + 𝟑/𝟒 × 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.