Question

2. A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

Answer 1

So probability will be 0.34

Explanation:

We have given that a university admitted 100 students

In which 34 students are from two year community program

25 students are from private four year institution

And rest that is 100-34-25 = 41 students from public four year institutions

Number of ways for selecting two students from two year community program that is, from 34 students

`=^(34)C_2`

And the number of ways in selecting the 2 students from total student
`=^(100)C_2`

So probability will be
`P=(^(34)C_2)/(^(100)C_2)=(17)/(50)=0.34`