In a test a student either guesses or copies or knows the answer to answer a multiple choice question with four choices. The probability that he makes a guess is 1 / 3 and the probability that he copies the answer is 1 / 6 . The probability that his answer is correct, given that he copied it is 1 / 8 . The probability that he knew the answer to the question, given that he answered it correctly is

Step-by-step solution

Let define the following events: E ₁ : Students gusses the answer to the question. E ₂ : Students copies the answer to the question. E ₃ : Students know the answer to the quesiton. E : Answer is correct. Here, P ( E ₁ )= 1 3 , P ( E ₂ )= 1 6 P ( E ₃ )=1- ( 1 3 + 1 6 )= 1 2 Since, the question is a multiple choice question with four choice. So the probability that the answer is correct when it is gussed, P ( E E₁ )= 1 4 Also, the probability that his answer is correct, given that he copied it is 1 8 P ( E E₂ )= 1 8