In a business class,10% of the students have never taken a statistics class,35% 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 at least one of your two group mates has had more than one semester of statistics?
A)0.45
B)0.203
C)0.798
D)0.55
E)0.303

Question

Quizplus · Accepted Answer

Let's first find the probability that both of your group mates have taken only one semester of statistics.

P(both have taken only one semester) = 0.35 x 0.35 = 0.1225

Therefore, the probability that at least one of your group mates has taken two or more semesters of statistics is 1 - 0.1225 = 0.8775.

However, we also need to consider the probability that you are paired with someone who has never taken a statistics class.

P(you are paired with someone who has never taken a statistics class) = 0.1

Therefore, the final probability that at least one of your group mates has had more than one semester of statistics is:

0.8775 - (0.1 x 0.35) = 0.798

So the answer is choice C.

In a Business Class,10% of the Students Have Never Taken