Answer:
No, P(high school | GPA above 3.0) ≠ P(high school)
Step-by-step explanation:
Given
See attachment for table
Required
Determine if High school and GPA above 3.0 are independent
Let
[tex]H \to[/tex] High school
[tex]G \to[/tex] GPA above 3.0
For both events to be independent, the following must be true
[tex]P(H\ |\ G) = P(H)[/tex]
From the table:
[tex]P(H) = \frac{H}{Total}[/tex]
[tex]P(H) = \frac{60}{100} = 0.60[/tex]
[tex]P(H | G) = \frac{H\ n\ G}{G}[/tex]
[tex]P(H | G) = \frac{14}{40} = 0.35[/tex]
The test for independence is as follows:
[tex]P(H\ |\ G) = P(H)[/tex]
By comparison
[tex]P(H\ |\ G) \ne P(H)[/tex]
i.e.
[tex]0.35 \ne 0.60[/tex]
Hence, both events are not independent
