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

Pr (neither of two groups) = 0.0225

Step-by-step 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