Respuesta :
Answer:
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:
[tex]A = a + (A \cap B)[/tex]
In which a is the number of students who are enrolled in the economics course but not mathematics and [tex]A \cap B[/tex] is the number of students enrolled in both those courses.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
129 are enrolled in both an economics and a mathematics course.
This means that [tex]A \cap B = 129[/tex].
216 are enrolled in a mathematics course
This means that [tex]B = 216[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]216 = b + 129[/tex]
[tex]b = 87[/tex]
320 are enrolled in an economics course
This means that [tex]A = 320[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]320 = a + 129[/tex]
[tex]a = 191[/tex]
We want
[tex]A \cup B = a + b + (A \cap B) = 191 + 87 + 129 = 407[/tex]
Probability:
[tex]P = \frac{407}{500} = 0.814[/tex]
81.4% probability that a freshman selected at random from this group is enrolled in an economics and/or a mathematics course
