A student answers a multiple-choice question with possible answers. The student knows the correct answer with probability ; if she knows it she picks it with probability , otherwise she picks randomly with probability each. Given that the student picked the correct answer, the probability that she knew it is
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A student answers a multiple-choice question with m possible answers. The student knows the correct answer with probability p; if she knows it she picks it with probability 1, otherwise she picks randomly with probability 1/m each. Given that the student picked the correct answer, the probability that she knew it is (A) p/[1 + (1-p)m] (B) p/[1 + (m-1)p] (C) mp/[1 + (1-p)m] (D) mp/[1 + (m-1)p]
Probability and Bayes' theorem has come up 190 times in 7 exams since 2004.
This question is on Total probability and Bayes' theorem, part of Probability and Bayes' theorem in Statistics.
Reversing a conditional probability and updating beliefs from evidence.
TestStop has 22 past-paper questions on this subtopic.
Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.