Question

A student answers a multiple-choice examination question that offers four possible answers. Suppose the probability that the student knows the answer to the question is 0.8 and the probability that the student will guess is 0.2. Assume that if the student guesses, the probability of selecting the correct answer is 0.25. If the student correctly answers a question, what is the probability that the student really knew the correct answer

Answer 1

Answer:

The value is $P(A | W) = 0.941$

Step-by-step explanation:

From the question we are told that

The probability that the student knows the answer to the question is $P(A) = 0.8$

The probability that that the student will guess is $P(G) = 0.2$

The probability that that the student get the correct answer given that the student guessed is $P(W /G) = 0.25$

Here W denotes that the student gets the correct answer

Generally it a certain fact that if the student knows the answer he would get it correctly

So the probability the the student got answer given that he knows it is

$P(W | A) = 1$

Generally from Bayes theorem we can mathematically evaluate the probability that the student knows the answer given that he got it correctly as follows

$P(A | W) = \frac{ P(A) * P(W | A )}{ P(A) * P(W | A) + P(G) * P(W| G)}$

=> $P(A | W) = \frac{ 0.8 * 1}{ 0.8 * 1+ 0.2 * 0.25}$

=> $P(A | W) = 0.941$