In a large introductory statistics lecture hall, the professor reports that 51% of the students enrolled have never taken a calculus course, 32% 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?

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Arclight Arclight · Answer 1 · 2019-08-06T17:05:08+02:00

Answer:

a) [tex]0.2601[/tex]

b) [tex]0.2401[/tex]

c) [tex]0.17[/tex]

Step-by-step explanation:

There are total three groups say A, B and C.

Lets suppose I am assigned to be a part of group C

a) neither has studied calculus

P(Group A neither studied calculus) [tex]*[/tex] P(Group A neither studied calculus)

[tex]= 0.51 * 0.51\\= 0.2601[/tex]

b) both have studied at least one semester of calculus

Probability of studying one or more than one semesters of calculus

[tex]= (1-0.51-0.32) + 0.32\\= 0.49[/tex]

P(Group A has studied calculus) [tex]*[/tex] P(Group A has studied calculus)

[tex]= 0.49*0.49\\= 0.2401[/tex]

c) at least one has had more than one semester of calculus

[tex]1- P(none one)[/tex]

[tex]= 1-(0.83*0.83)\\= 0.311[/tex]

[tex]= 1- 0.51-0.32\\= 0.17\\[/tex]