31. a statistics class has 26 students. the instructor would like to select a random sample of 3 students to work together on a group project. a. how many different samples are possible? b. if 13 of the 26 students in class are freshmen, what is the probability that all 3 of the selected students are freshmen?



Answer :

PNaik

a. 2600 ways different samples are possible.

b. 0.11  is the probability that all 3 of the selected students are freshmen.

total student = 26

3 students are randomly selected  on group project

a.   the possible  different sample are

[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]

      =  [tex]\frac{26}{3 (23)}[/tex]

     = 2600 ways.

b.  13 students are freshmen  

Pr ( 3  selected students  is freshman)

[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

To learn more about probability, refer;

https://brainly.com/question/14210034

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