Question

Among 500 freshmen pursuing a business degree at a university, 311 are enrolled in an economics course, 243 are enrolled in a mathematics course, and 135 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following?

a) an economics and/or a mathematics course.
b) exactly one of these two courses.
c) neither an economics course nor a mathematics course.

Answer 1

Let A = Economics, B = Mathematics

n(A) = 311, n(B) = 243,
`$n(A \cap B) = 135$`

a). So,
`$n(A \cup B) = n(A) +n(B) - n(A \cap B)$`

= 311 + 243 - 135

= 419

b). n(A only) = 311 - 135

= 176

n(B only) = 243 - 135

= 108

Exactly one of these two courses

`$=(176+108)/(500)$`

= 0.568

c). Neither economics nor mathematics

`$=(500-419)/(500) $`

`$=(81)/(500)$`

= 0.162