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In a multiple-choice test with four alternatives, a candidate responds in one of three ways: by guessing, by copying, or by actually knowing the answer. The probability that he guesses is 1/3, and the probability that he copies is 1/6. If he copies, the chance that his response is correct is 1/8. Given that his final response is correct, the probability that he knew the answer is:
- 24/29
- 1/4
- 3/4
- 1/2
Correct answer: 24/29
Solution
P(know)=1-1/3-1/6=1/2. P(correct)=(1/3)(1/4)+(1/6)(1/8)+(1/2)(1)=1/12+1/48+1/2=29/48. By Bayes, P(know|correct)=(1/2)/(29/48)=24/29.
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