In a large introductory statistics lecture hall, the professor reports that 60% of the students enrolled...
In a large introductory statistics lecture hall, the professor reports that 60% of the students enrolled have never taken a calculus course, 20% 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, a) neither has studied calculus? b) both have studied at least one semester of calculus? c) at least one has had more than one semester of calculus?
Homework Answers
a) Probability that neither of the two of our group members have studied calculus is computed here as:
= 0.62 = 0.36
Therefore 0.36 is the required probability here.
b) Probability that both have studied at least one semester of calculus
= ( 1 - 0.6)2 = 0.42 = 0.16
Therefore 0.16 is the required probability here.
c) Probability that at least one has had more than one semester of calculus is computed here as:
= 1 - Probability that both have less than or equal to 1 semester of calculus
= 1 - (0.6 + 0.2)2 = 1 - 0.64 = 0.36
Therefore 0.36 is the required probability here.
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