Question

A two-way frequency table shows grades for students in college and students in high school.

Answer 1

If two events A and B are independent, then P(A | B) = P(A)

P(high school | GPA above 3.0) = 14/40 = 0.35
P(high school) = 60/100 = 0.6

Therefore, the two events are not independent because P(high school | GPA above 3.0) ≠ P(high school)

Answer 2

Answer: No, P(high school | GPA above 3.0) ≠ P(high school)

Step-by-step explanation:

Since we have given that

A two-way frequency table.

We need to show that "being in High School (H)" and "GPA above 3.0 (G)" are independent events:

So, for independent events we need to show that

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

First we will calculate the "Conditional probability" :

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

And Probability of getting "Being in High school ":

$\frac{60}{100}\\\\=0.6$

And we get that

$P(H\mid G)\neq P(H)$

Hence,  They are not independent events.

No, P(high school | GPA above 3.0) ≠ P(high school)