Question

Based on this data, are "being in high school" and "GPA above 3.0" independent events? Yes, P(high school ∩ GPA above 3.0) = P(high school) ⋅ P(GPA above 3.0) No, P(high school ∩ GPA above 3.0) = P(high school) ⋅ P(GPA above 3.0) Yes, P(high school ∩ GPA above 3.0) ≠ P(high school) ⋅ P(GPA above 3.0) No, P(high school ∩ GPA above 3.0) ≠ P(high school) ⋅ P(GPA above 3.0)

Answer 1

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

$H \to$ High school

$G \to$ GPA above 3.0

For both events to be independent, the following must be true

$P(H\ |\ G) = P(H)$

From the table:

$P(H) = \frac{H}{Total}$

$P(H) = \frac{60}{100} = 0.60$

$P(H | G) = \frac{H\ n\ G}{G}$

$P(H | G) = \frac{14}{40} = 0.35$

The test for independence is as follows:

$P(H\ |\ G) = P(H)$

By comparison

$P(H\ |\ G) \ne P(H)$

i.e.

$0.35 \ne 0.60$

Hence, both events are not independent