In a business class,15% of the students have never taken a statistics class,40% have taken only one semester of statistics,and the rest have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.Assume everyone in the group is independent.What is the probability that neither of your two group mates has studied statistics?
A)0.45
B)0.023
C)0.15
D)0.85
E)0.30

Question

Quizplus · Accepted Answer

Let X be the number of group mates that have studied statistics, then X follows a hypergeometric distribution with N = 100 (total students), M = 15 (students who have never taken statistics), and n = 2 (number of group mates). The probability that neither of your two group mates has studied statistics is:
P(X = 0) = (M choose n)/(N choose n) = (15 choose 2)/(100 choose 2) = 105/4950
Since there are 98 other students who could potentially be your group mates, we need to multiply this probability by the probability that none of these 98 students are assigned to your group, which is (97 choose 1)/(98 choose 2) = 97/4851 (assuming that no student is assigned to more than one group). Therefore, the overall probability is:
P(neither group mate has studied statistics) = P(X = 0) * (97/4851) = 105/4950 * 97/4851 ≈ 0.023.

In a Business Class,15% of the Students Have Never Taken