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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?
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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