Among 500 freshmen pursuing a business degree

Ответ:

jordynnmarelich9519

20.01.2022

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

Step-by-step 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:

$P = \frac{407}{500} = 0.814$

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

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