Question

PROBLEM 01: There are 100 students waiting in line to get student IDs. Of these, 50 are from Indiana, 45 are freshmen, and 20 are neither freshmen nor from Indiana. How many of the students are freshmen who are not from Indiana?

Answer 1

Answer: 30

Explanation:

Let U be the total number of students waiting in line to get student IDs, A represents the number of students from Indiana and B represents the number of students are freshmen.

Given : n(U)=100

n(A)=50

n(B)=200

`n(A'\cup B')=20`

`\text{Now, }n(A\cup B)= n(U)-n(A'\cup B')\\\\\Rightarrow\ n(A\cup B)=100-20=80`

Also,
`n(A\cup B)=n(A)+n(B)-n(A\cap B)`

`\Rightarrow\ 80=50+45-n(A\cap B)\\\\\Rightarrow\ n(A\cap B)=95-80=15`

The number of students are freshmen who are not from Indiana is given by :-

`n(B)-n(A\cap B)=45-15=30`

Hence, there are 30 freshmen students who are not from Indiana