Question

Among 500 freshmen pursuing a business degree at a university, 320 are enrolled in an economics course, 216 are enrolled in a mathematics course, and 129 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

Answer 1

81.4% probability that a freshman selected at random from this group is enrolled in an economics and/or a mathematics course

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Total outcomes:

500 freshmen

Desired outcomes:

Enrolled in an economics and/or a mathematics course

Build the Venn's diagram.

I am going to say that:

A is the number of students enrolled in the economics course.

B is the number of students enrolled in the mathematics course.

We have that:

`A = a + (A \cap B)`

In which a is the number of students who are enrolled in the economics course but not mathematics and
`A \cap B` is the number of students enrolled in both those courses.

By the same logic, we have that:

`B = b + (A \cap B)`

129 are enrolled in both an economics and a mathematics course.

This means that
`A \cap B = 129`.

216 are enrolled in a mathematics course

This means that
`B = 216`

`B = b + (A \cap B)`

`216 = b + 129`

`b = 87`

320 are enrolled in an economics course

This means that
`A = 320`

`A = a + (A \cap B)`

`320 = a + 129`

`a = 191`

We want

`A \cup B = a + b + (A \cap B) = 191 + 87 + 129 = 407`

Probability:

`P = (407)/(500) = 0.814`

81.4% probability that a freshman selected at random from this group is enrolled in an economics and/or a mathematics course