Question

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?

Answer 1

Answer:

a) $0.2601$

b) $0.2401$

c) $0.17$

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) $*$ P(Group A neither  studied​ calculus)

$= 0.51 * 0.51\\= 0.2601$

b)  both have studied at least one semester of​ calculus

Probability of studying one or more than one semesters of calculus

$= (1-0.51-0.32) + 0.32\\= 0.49$

P(Group A has studied​ calculus) $*$ P(Group A has studied​ calculus)

$= 0.49*0.49\\= 0.2401$

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

$1- P(none one)$

$= 1-(0.83*0.83)\\= 0.311$

$= 1- 0.51-0.32\\= 0.17$