At a particular college, 66% of the students live in campus housing. If 5 students are in line at the
Campus bookstore, what is the probability that exactly 2 of them live in campus housing? Round to
Four decimal places, if necessary.
A)0.2568
B)0.3424
C)0.1712
D)0.0342

Question

Quizplus · Accepted Answer

The probability of a student living in campus housing is 0.66, therefore the probability of a student not living in campus housing is 0.34. 
Using the binomial distribution formula, where n=5 (total number of students in line), p=0.66 (probability of success), and x=2 (number of students living in campus housing in the line):
P(X=2) = (5 choose 2)(0.66)^2(0.34)^3 
P(X=2) = 0.1712 (rounded to four decimal places) 
Therefore, the probability that exactly 2 of the 5 students in line live in campus housing is 0.1712. The best choice is C.

At a Particular College, 66% of the Students Live in Campus