when answering a question on multiple choice test with 4 answeres, a student either knows the answer or he guesses. The probability that he knows the answer is 0.80. What is the probability that a student knew the answer to a question given that he answered it correctly?

0.9412

Explanation:

Let's assume that there are 4 choices to each question and 1 of them is correct.

Hence, probability of answering a question correctly = P (A) = / frac{1}{4} = 0.25

Probability of students who knows the answer = P (B) = 0.80

Hence, Probability of students who guesses the answer = P (B^c) = 1-0.80 = 0.20

We need to find out probability that a student knew the answer to a question given that he answered it correctly i. e. P (B|A)

As per Baye's Theorem, P (B|A) = / fracB) P (B) P (A

P (A|B) = Probability of answering a question correctly given that the student knows the answer = 1

Hence, P (B|A) = / frac{0.80 / times 1}{0.80 / times 1+0.25 / times 0.20} = 0.9412