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 semes- ter 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 some calculus?

Answer 1

To find the probability that the first groupmate you meet has studied some calculus, we need to calculate the probability that at least one of the two other groupmates has studied calculus.

Step-by-step explanation:

To find the probability that the first groupmate you meet has studied some calculus, we need to calculate the probability that at least one of the two other groupmates has studied calculus.

Let's start by finding the probability that all three groupmates have never taken a Calculus course. Since the probability that a student has never taken Calculus is 55%, the probability that all three groupmates have never taken Calculus is 0.55 * 0.55 * 0.55 = 0.166375

Therefore, the probability that at least one of the two other groupmates has studied calculus is 1 - 0.166375 = 0.833625.

Answer 2

There is a 45% probability that the first groupmate you meet has studied some calculus.

Step-by-step explanation:

We have these following percentages:

55% of the students enrolled have never taken a Calculus course

32% have taken only one semester of Calculus

R is the rest, those have taken two or more semesters of Calculus.

The sum of the percentages must be 100, so:

`55 + 32 + R = 100`

`R = 13`

13% have taken two or more semesters of Calculus.

What is the probability that the first groupmate you meet has studied some calculus?

This are those who either have taken only one semester of Calculus, or two or more.

So

32% + 13% = 45%

There is a 45% probability that the first groupmate you meet has studied some calculus.