Peter is a Computer Science major, but has lots of friends who are IE majors. In
ID: 3306959 • Letter: P
Question
Peter is a Computer Science major, but has lots of friends who are IE majors. In Peter’s Computer Science class, there are 27 other students in the class with Peter, 13 of whom are IE majors. During the semester, students will be working on a project in teams of 4 students. Suppose the students are divided into teams at random, so that Peter’s team contains Peter and three other randomly-chosen students. All students are assigned to exactly one team. Round your answers to 4 significant figures.
a. Find the probability that at least 2 out of 3 students on Peter's team are IE majors.
b. Find the probability that there is at least 1 IE major on Peter's team.
c. Find the probability that at most 2 out of 3 students on Peter's team are IE majors.
Explanation / Answer
Number of students excluding peter = 26
Number of IE majors = 13
a) P(at least 2 out of 3 students on Peter's team are IE majors) = P(2 IE majors) + P(3IE majors)
= 13C2x13C1/26C3 + 13C3/26C3
= 0.39 + 0.11
= 0.5
b) P (at least 1 IE major on Peter's team) = 1 - P(all non IE majors)
= 1 - 13C3/26C3
= 1 - 0.11
= 0.89
c) P(at most 2 out of 3 students on Peter's team are IE majors) = 1 - P(3 IE majors)
= 1 - 13C3/26C3
= 1 - 0.11
= 0.89
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