A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who 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.
If 35% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that neither of the first two groupmates you meet has studied any statistics?
A)0.35
B)0.70
C)0.65
D)0.123
E)0.40

Question

Quizplus · Accepted Answer

The probability that neither of the first two groupmates has studied any statistics is calculated by multiplying the probability of selecting a student who has never taken a statistics class twice, as the selections are independent. Given that 35% of the students have never taken a statistics class, the probability for each selection is 0.35. Therefore, the probability for two such selections is $0.35 \times 0.35 = 0.1225$, which rounds to 0.123.

A Professor Divided the Students in Her Business Class into Three