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

The value is

Step-by-step explanation:

From the question we are told that

The probability that the student knows the answer to the question is

The probability that that the student will guess is

The probability that that the student get the correct answer given that the student guessed is

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

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

=>

=>

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!