In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90 % . If he gets the correct answer to a question, then what is the probability that he was guessing ?

Step-by-step solution

Let E₁ be the event that the student knows the answer and E₂ be the event that the student guesses the answer. Let A be the event that the student gets the correct answer. From the given information: P(E₁) = 90 100 = 9 10 P(E₂) = 1 - P(E₁) = 1 10 If the student knows the answer, the probability of getting it correct is 1 , so P(A|E₁) = 1 . If the student guesses, since there are 4 options with only one correct, P(A|E₂) = 1 4 . The probability that the student was guessing given that the answer is correct is P(E₂|A)