Question

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability What is the probability that the student knows the answer given that he answered it correctly?

Answer 1

Let E₁ and E₂ be the respective events that the student knows the answer and he guesses the answer.

Let A be the event that the answer is correct.

The probability that the student answered correctly, given that he knows the answer, is 1.

∴ P (A|E₁) = 1

Probability that the student answered correctly, given that he guessed, is .

The probability that the student knows the answer, given that he answered it correctly, is given by .

By using Bayes’ theorem, we obtain