Question

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?

Answer 1

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:
$E(X)=0\times0.1379+1\times0.3819+2\times0.341+3\times0.1213+4\times0.017$$+5\times0.0008+6\times0.000007=1.4998$
The answer is: 1.4998