2.) In a large introductory statistics lecture hall, the professor reports that

Question

2.) In a large introductory statistics lecture hall, the professor reports that 51% of the students enrolled have never taken a calculus course, 30% have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group.

a) What is the probability that of your other two groupmates, neither has studied calculus? (type an integer or decimal)

b) What is the probablity that both of your other two groupmateshave studied at least one semester of calculus? (type an integer or decimal)

c) What is the probablity that at least one of your two groupmates has had more than one semester of calculus? (type an integer or decimal)

Explanation / Answer

a)probability that of your other two groupmates, neither has studied calculus=0.51*0.51=0.2601

b) probablity that both of your other two groupmateshave studied at least one semester of calculus =(1-0.51)*(!-0.51)=0.2401

c)probablity that at least one of your two groupmates has had more than one semester of calculus

=1-P(none have taken more than 1 semester of calculus ) =1-(0.51+0.30)2 =0.3439

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