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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

1 Answer

5 votes

Answer:

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

User Panjiyar Rahul
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