Venn Diagram

Question

500 freshman at USC are pursuing a business degree.

 

300 are enrolled in economics

225 in mathematics

140 in both courses

 

what is the probability a freshman selected will be enrolled in:

 

exactly one of the courses?

neither course?

Answer 1

300 (taking economics) - 140 (also taking math) = 160 (solely economics)

225 (taking math) - 140 (also taking economics) = 85 (solely math)

 

160 + 85 = 245 (total only taking one course)

500 (total students) - 245 (taking one) - 140 (taking both) = 115 (neither course)

Answer 2

1. 300 are enrolled in economics, of which 140 are also enrolled in math.  So 160 are enrolled in economics and NOT in math.

 

225 are enrolled in math, of which 140 are also enrolled in economics.  So 85 are enrolled in math and NOT in economics.

 

So 160 + 85 = 245 are enrolled in either math or economics, but not both.

 

 

2. The number enrolled in either course (one or both) is 300 + 225 - 140 = 385.  So 500 - 385 = 115 are not enrolled in either course.