In an entrance test there are multiple choice questions, with four possible answer to each question of which one is correct, The probability that a student knows the answer to a question is 90%, If the student gets the correct answer to a question, then the probability that he was guessing is

Concept:

Bayes' Theorem:

Let E1, E2, ….., En be n mutually exclusive and exhaustive events associated with a random experiment and let S be the sample space.

Let A be any event which occurs together with any one of E1 or E2 or … or En such that P(A) ≠ 0.

Then 

Calculation:

Let E₁: He knows the answer

E2: He does not know the answer

X: He gets the correct answer.

Therefore, P (E1) = 90% = 

P (E2) =  

P (X | E1)  = 1

P (X | E2)  = 

As we know that according to Bayes' theorem: