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) (3 points) two or more semesters of Calculus? (b) (3 points) some Calculus? (c) (3 points) no more than one semester of Calculus? You are again assigned to be part of a group of three students from the class described above. What is the probability that of your other two groupmates, (d) (3 points) neither has studied Calculus? (e) (3 points) both have studied at least one semester of Calculus? (f) (4 points) at least one has had more than one semester of Calculus?

          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) (3 points) two or more semesters of Calculus?
(b) (3 points) some Calculus?
(c) (3 points) no more than one semester of Calculus?
You are again assigned to be part of a group of three students
from the class described above. What is the probability that of
your other two groupmates,
(d) (3 points) neither has studied Calculus?
(e) (3 points) both have studied at least one semester of
Calculus?
(f) (4 points) at least one has had more than one semester of
Calculus?

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Added by Troy G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jacob Fry

03/03/2023

Step 1

Since 55% have never taken Calculus and 32% have taken only one semester, the remaining percentage must have taken two or more semesters. 100% - 55% - 32% = 13% (a) The probability that the first groupmate you meet has studied two or more semesters of Calculus Show more…

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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) (3 points) two or more semesters of Calculus? (b) (3 points) some Calculus? (c) (3 points) no more than one semester of Calculus? You are again assigned to be part of a group of three students from the class described above. What is the probability that of your other two groupmates, (d) (3 points) neither has studied Calculus? (e) (3 points) both have studied at least one semester of Calculus? (f) (4 points) at least one has had more than one semester of Calculus?

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00:01 So in this question we're told that the probability that a student has never taken a calculus course, so probability never taken calculus course is 55%.

00:12 The probability that they've taken one semester of calculus is 32%, and the probability of having taken two or more is the rest.

00:28 So that's 55 plus 32 is 87, so we have 13 % remaining.

00:35 Okay, so now part a, what's the probability that the first groupmate you meet has studied the following? well, the first groupmate you meet, so first group mate is a random member of the population.

01:00 So the probabilities associated with them are just the probabilities associated with a random person in the class.

01:06 So what that means is that the probability that the random, that the first group mate has studied 2 plus semesters of calculus, it's just going to be the probability that anyone has, which is 13%.

01:26 Part b, what's the probability that they have studied some calculus? so the probability that the first has studied some is 1 minus the probability that the first has studied none.

01:39 So that's 1 minus 55%, which is 45%.

01:49 Part c, what's the probability that they've studied no more than one semester of calculus? so first, no more than one.

02:02 That's going to be the probability that they've studied none, plus the probability that they've studied one.

02:08 So that is 55 plus 32 is 87%.

02:16 So now you're again assigned to be part of a group of three.

02:19 What's the probability that of your other two groupmates, what's the probability that neither of two have any calculus? well, that's going to be the probability that they both have studied none, and if they're independently chosen from this class, that's just going to be 0 .55 squared, which is 0 .3025...

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