Question

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

Answer 1

Pr(neither of two groups) = 0.0225

Explanation:

Given:

15% of the students have never taken a statistics class = Pr(none)

Pr(none) = 0.15

40% have taken only one semester of statistics =Pr(one semester)

Pr(one semester) = 0.40

the rest have taken two or more semesters of statistics = Pr(two or more semester)

Pr(two or more semester) = 1 - [Pr(one semester) + Pr(none) ]

Pr(two or more semester) = 1-(0.40+0.15) = 1 - 0.55

Pr(two or more semester) = 0.45

Where Pr = probability

Let probability that neither of your two group mates has studied statistics = Pr(neither of two groups)

=Pr(none in group 1) ×Pr(none in group 2)

= 0.15 × 0.15

Pr(neither of two groups) = 0.0225