Question

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?

Answer 1

0.9412

Step-by-step 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) =\fracB)B)+P(A

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