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Question
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let `3/5` be the probability that he knows the answer and `2/5` be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability `1/3`. What is the probability that the student knows the answer, given that he answered it correctly?
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Solution
Let B1 be the event student knows the answer
B2 be the event student guesses the answer
E = Event answer is correct
P(B1) = `3/5`
P(B2) = `2/5`
`P(E/B_1)` = 1
`P(E/B_2) = 1/3`
`P(B_1/E) = (P(B_1)P(E/B_1))/(P(B_1)P(E/B_1) + P(B_2)P(E/B_2))`
= `(3/5 xx 1)/(3/5 xx 1 + 2/5 xx 1/3)`
= `(3/5)/((9 + 2)/15)`
= `9/11`.
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