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?

Answer 1

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`.