Question

In answering a question on a multiple choice test, a student either company the answer or guesses or he knows the answer. Let 1/6 be the probability that he copy the answer 1/3 and be the probability that he guesses Assuming that a student who copy the answer will be correct with probability 1/8. What is the probability that the student knows the answer given that he answered it correctly.

Answer 1

Probability that student guesses the answer 

P(A) = 1/3

Probability that student copies the answer 

P(B) = 1/6

Probability that student knows the answer 

P(C) = 1 - 1/3 - 1/6

= (6 - 2 - 1)/6 = (6 - 3)/6

= 3/6 = 1/2

Let E is the event that answer is correct

Probability that student knows the answer and answered correctly