Question

A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. Find the requested probability. If 55% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied some statistics

Answer 1

the probability that the first groupmate you meet has studied some statistics is 0.45

Explanation:

From the information given :

A professor divided the students in her business class into three groups

Let consider then to be :

Group Statistics Class

A Never taken a statistics class

B Taken one statistics class

C Taken two or more statistics class.

If 55% of the students have never taken a statistics class,

Then ;

P(A) = 0.55

25% have taken only one semester of a statistics class

Then P(B) = 0.25

and the rest have taken two or more semesters of statistics

Then P(C) = 1 - 0.55 -0.25

P(C) = 1 - 0.80

P(C) = 0.20

The objective is to determine the probability that the first groupmate you meet has studied some statistics

The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)

Let the probability of the first groupmate you meet that has studied some statistics be P(D)

Then P(D) = 1 - P(A)

P(D) = 1 - 0.55

P(D) = 0.45

the probability that the first groupmate you meet has studied some statistics is 0.45