Question

In a sociology class there are 1414 sociology majors and 1111 non-sociology majors. 33 students are randomly selected to present a topic. What is the probability that at least 22 of the 33 students selected are non-sociology majors? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer:
`0.4065`

Explanation:

Given : In a sociology class there are 14 sociology majors and 11 non-sociology majors.

Total students = 14+11=25

Number of students are randomly selected = 3

Then, the number of ways to select 3 students from 25 students :-

`^(25)C_3=(25!)/((25-3)!3!)=(25*24*23*22!)/(22!3!)\\\\=2300`

Number of ways to select at least 2 of the 3 students re non-sociology majors :-

`^(14)C_1*^(11)C_2+^(14)C_0* ^(11)C_(3)\\\\=(14)*(11!)/(2!(11-2)!)+(1)*(11!)/(3!(11-3)!)\\\\=(14)(11*5)+(11*10*9)/(6)\\\\=770+165=935`

The probability that at least 2 of the 3 students selected are non-sociology majors will be :-

`(935)/(2300)=0.40652173913\approx0.4065`