In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4. What is the probability that a student knows the answer given that he answered it correctly?

Question

Philoid · Accepted Answer

Let us assume U₁, U_2, and A be the events as follows:

U₁ = Knowing the answer

U₂ = Guessing the answer

A = Answering the question correctly

From the problem

⇒

⇒ P(A|U₁) = P(Answering the question correctly by knowing the answer)

⇒ P(A│U₁ ) = 1

⇒ P(A|U₂) = P(Answering the question correctly by guessing the answer)

⇒

Now we find

P(U₁|A) = P(The answer is known given that he answerd the question correctly)

Using Baye’s theorem:

⇒

∴ The required probability is.