Question

1. A survey conducted by the Bureau of Labor Statistics found that 64% of the high

school graduating class of 2003 went on to college the following year, while 55% of the
class was working. Furthermore, 92% were either in college or working or both.
a) What percentage went on to college and work at the same time?
b) What percenlage went on to college but not work?

Answer 1

(a)27%

(b)37%

Explanation:

Let percentage of those who went to college, n(C)=64%

Let percentage of those who work, n(W)=55%

Since, 92% were either in college or working or both,
`n(C\cup W)=92\%`

From Set Theory:

(a)Percentage went on to college and work at the same time

`n(C\cup W)=n(C)+n(W)-n(C\cap W)\\92=64+55-n(C\cap W)\\n(C\cap W)=121-92\\n(C\cap W)=27\%`

The percentage who went on to college and work at the same time is 27%.

(b)Percentage went on to college but not work

`n(C\cap W')=n(C)-n(C\cap W)\\=64-27\\=37\%`

The percentage who went on to college but not work is 37%.