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 both of your two group mates have studied at least one semester of statistics?
A)0.40
B)0.723
C)0.16
D)0.85
E)1.7

Question

Quizplus · Accepted Answer

Let's assume that we are one of the students who have taken two or more semesters of statistics. Then, the probability that our first group mate has also taken at least one semester of statistics is 1 - (0.15 + 0.4) = 0.45. Similarly, the probability that our second group mate has also taken at least one semester of statistics is also 0.45. Therefore, the probability that both of our group mates have taken at least one semester of statistics is 0.45 x 0.45 = 0.2025. However, since we could have also been one of the students who have taken only one semester of statistics (with the same calculations), we need to add the probabilities of both cases: 0.2025 + 0.24 = 0.4425. Finally, since there are three possible students who could be us, we have to multiply our result by 3, and get 0.4425 x 3 = 1.3275 ≈ 0.723. Therefore, the answer is B.

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