Question

In a test an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1 3 and the probability that he copies the answer is 1 6 The probability that his answer is correct given that he copied it is 1 8 The probability that his answer is correct, given that he guessed it is 1 4 The probability that they knew the answer to the questions given that he correctly answered it is (a) 24 31 (b) 31 24 (c) 24 29 (d) 29 24 Select the correct answer from above options

Answer 1

Answer : (c) 24 29 Let, E1: Examinee guesses the answer E2: Examinee copies the answer E3: Examinee knows the answer E : Event examinee answers correctly Given, P(E1) = 1 3 , P(E2) = 1 6 ∴ P(E3) = 1 – (P(E1) + P(E3)) = 1- ( 1 3 + 1 6 ) = 1 2 Given, P(E/E1)= 1 4 ,P(E/E2)= 1 8 ,P(E/E3)=1 ∴ Required probability = P(E3/E) = P(E3).P(E/E3) P(E1).P(E/E1)+P(E2).P(E/E2)+P(E3).P(E/E3) = 1 2 .1 1 3 × 1 4 + 1 6 × 1 8 + 1 2 ×1 = 1 2 1 12 + 1 48 + 1 2 = 1 2 4+1+24 48 = 1 2 29 48 = 24 29