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: $0.4065$

Step-by-step 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 :-

$^{25}C_3=\dfrac{25!}{(25-3)!3!}=\dfrac{25\times24\times23\times22!}{22!3!}\\\\=2300$

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

$^{14}C_1\times^{11}C_2+^{14}C_0\times ^{11}C_{3}\\\\=(14)\times\dfrac{11!}{2!(11-2)!}+(1)\times\dfrac{11!}{3!(11-3)!}\\\\=(14)(11\times5)+\dfrac{11\times10\times9}{6}\\\\=770+165=935$

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

$\dfrac{935}{2300}=0.40652173913\approx0.4065$