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.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 consider the three possible scenarios for the composition of the group:

1. All three students have never taken a statistics class. The probability of this happening is:
(0.15)*(0.15)*(0.15) = 0.003375

2. Two of the students have never taken a statistics class and one has taken at least one semester. The probability of this happening is:
(0.15)*(0.15)*(0.85) + (0.15)*(0.85)*(0.15) + (0.85)*(0.15)*(0.15) = 0.03825

3. All three students have taken at least one semester of statistics. The probability of this happening is:
(0.4)*(0.4)*(0.4) = 0.064

So, the probability that both of your two group mates have studied at least one semester of statistics is the complement of scenario 1:
1 - 0.003375 = 0.996625
And the probability that both of your two group mates have studied at least one semester of statistics given that at least one of them has studied statistics is:
0.064/0.9025 (sum of probabilities of scenario 2 and 3) = 0.0710363 (rounded to three decimal places)
Therefore, the answer is B) 0.723.

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