In a history class, students take a weekly multiple choice quiz consisting of 6 questions, each with 4 possible answers. if a student randomly guesses at the answer to each question for every quiz, then what is the mean number of correct answers the student will get on each quiz?

There are 24 possible answers, 6 are correct answers and 18 are incorrect answers. By use of the hypergeometric distribution the probabilities of each possible number of randomly selected correct answers can be found, as follows:
P(0) = 0.1379, P(1) = 0.3819, P(2) = 0.341, P(3) = 0.1213, P(4) = 0.017, P(5) = 0.0008, P(6) = 0.000007.
The expected or mean number of correct answers is found from:

The answer is: 1.4998