Question

In a small class of twelve students, two did not do the homework. The professor randomly selects half of the students to present solutions to homework problems on the board. Find the expected value for the number of selected students that did not do the assignment.

Answer 1

Number of students in the class = 12

Number of students that did not do the home work = 2

Probability of a randomly selected student did not do the home work

= Number of students that did not do the home work / Number of students in the class

=2/12 = 1/6

Number of students selected by the professor to  to present solutions to homework problems on the board : n = 6

X : Number of selected students that did not do the assignment.

X follows binomial distribution with n= 6 and p = 1/6

Expected Value of Binomial distribution: E(X) = np

Therefore,

Expected value for the number of selected students that did not do the assignment : E(X) = np = 6 x (1/6) =1

Expected value for the number of selected students that did not do the assignment = 1