Question

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 the student knows the answer given that he answered it correctly?

Answer 1

Let E₁: know the answer; E₂: be the placement of students.

E: The student gives the correct answer.

Then P(E₁) = `3/4`, P(E₂) = `1/4` or P(E|E₁) = 1, P(E|E₂) = `1/4`

Hence, from Baye's theorem

P(E₁|E) = `(P(E_1) xx P(E|E_1))/(P(E_1) xx P(E|E_1) + P(E_2) xx P(E|E_2)`

= `(3/4 xx 1)/(3/4 xx 1+ 1/4 xx 1/4)`

= `(3/4)/(3/4 + 1/4)`

= `(3/4)/(13/16)`

= `3/4 xx 16/13`

= `12/13`