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

a)
`0.2601`

b)
`0.2401`

c)
`0.17`

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\\`