Question
In a large introductory statistics lecture hall, the professor reports that 60% of the students enrolled have never taken a calculus course, 29% 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. What is the probability that of your other two groupmates, neither has studied calculus? both have studied at least one semester of calculus? at least one has had more than one semester of calculus?The probability that neither of your other two groupmates has studied calculus is 0.36. (Round to four decimal places as needed.) The probability that both of your other two groupmates have studied at least one semester of calculus is 0.16. (Round to four decimal places as needed.) The probability that at least one of your other two groupmates has had more than one semester of calculus is 0.4782. (Round to four decimal places as needed.)
Answer
a) 0.6^2 = 0.36
b) 0.4^2 = 0.16
c)
Let A and B be the partners)
P(A having more than one semester of calculus) = 1 – (0.60 + 0.29) = 0.11
P(B having more than one semester of calculus) = 0.11
P( A U B) = P(A) + P(B) – P(A n B)
= 0.11 + 0.11 – (0.11*0.11)
= 0.2079
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