In a test, an examinee either guesses or copies or knows that answer to a multiple-choice question which has four choices. The probability that he makes a guess is 1/3, and the probability that he copies is 1/6. The probability that his answer is correct, given the copied it, is 1/8. Find the probability that he knew the answer to the question, given that he answered it correctly.

P(g) = probability of guessing = 1/3

P(c) = probability of copying = 1/6

P(k) = probability of knowing = 1 – 1/3 – 1/6 = 1/2

(Since the three-event g, c and k are mutually exclusive and exhaustive)

P(w) = probability that answer is correct

P(k/w)=(P(w/k).P(k))/(P(w/c)P(c)+P(w/k)P(k)+P(w/g)P(g)) (using Baye’s theorem)

= (1×1/2)/((1/8,1/6)+(1×1/2)+(1/4×1/3) )=24/29


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