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?

Explanation

Let `P(A)` is the probability that the student knows the answer and `P(A')` is the probability he guesses the answer.

Let `P(B)` is the probability he answers correctly.

Then,

`P(A) = 3/5, P(A') = 2/5`

`P(B/A') = 1/3, P(B/A) = 1`

We have to find `P(A/B)`.

From Bayes Theorem,

`P(A/B) = (P(B/A)P(A))/(P(B/A)P(A)+P(B/A')P(A'))`

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