When answering a question on multiple choice test with 4 answeres, a student either knows the answer or he guesses. the probability that he knows the answer is 0.80. what is the probability that a student knew the answer to a question given that he answered it correctly?

0.9412

Explanation:

Let's assume that there are 4 choices to each question and 1 of them is correct.

Hence, probability of answering a question correctly = P(A) =\frac{1}{4} = 0.25

Probability of students who knows the answer = P(B) =0.80

Hence, Probability of students who guesses the answer = P(B^c) =1-0.80 = 0.20

We need to find out probability that a student knew the answer to a question given that he answered it correctly i.e. P(B|A)

As per Baye's Theorem, P(B|A) =\frac{P(B)P(A|B)}{P(B)P(A|B)+P(A|B^c) P(B^c)}

P(A|B) = Probability of answering a question correctly given that the student knows the answer = 1

Hence, P(B|A) =\frac{0.80 \times 1}{0.80 \times 1+0.25 \times 0.20} = 0.9412

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