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Question

# In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability What is the probability that the student knows the answer given that he answered it correctly?

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Solution

## Let E1 and E2 be the respective events that the student knows the answer and he guesses the answer. Let A be the event that the answer is correct. The probability that the student answered correctly, given that he knows the answer, is 1. ∴ P (A|E1) = 1 Probability that the student answered correctly, given that he guessed, is . The probability that the student knows the answer, given that he answered it correctly, is given by . By using Bayes’ theorem, we obtain

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