Question

In a large Introductory Statistics lecture hall, the professor reports that 55% 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. What is the probability that the first groupmate you meet has studied

a) two or more semesters of Calculus?
b) some Calculus?
c) no more than one semester of Calculus?

Answer 1

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

Answer 2

a) There is a 13% probability that a student has taken 2 or more semesters of Calculus.

b) 45% probability that a student has taken some calculus.

c) 87% probability that a student has taken no more than one semester of calculus.

Explanation:

We have these following probabilities:

A 55% that a student hast never taken a Calculus course.

A 32% probability that a student has taken one semester of a Calculus course.

A 100-(55+32) = 13% probability that a student has taken 2 or more semesters of Calculus.

a) two or more semesters of Calculus?

There is a 13% probability that a student has taken 2 or more semesters of Calculus.

b) some Calculus?

At least one semester.

So there is a 32+13 = 45% probability that a student has taken some calculus.

c) no more than one semester of Calculus?

At most one semester.

So 55+32 = 87% probability that a student has taken no more than one semester of calculus.