Question

A two-way frequency table shows grades for students in college and students in high school: High school College Total GPA above 3.0 14 26 40 GPA below 3.0 46 14 60 60 40 100 Based on this data, are "being in high school" and "GPA above 3.0" independent events?

Answer 1

No, the two events "being in high school" and "GPA above 3.0" are not independent.

Explanation:

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

P(high school | above 3.0) =
`(14)/(40)=0.35`

P(high school) =
`(60)/(100)=0.6`

So,0.35 ≠ 0.6

Since P(high school | above 3.0) ≠ P(high school), the events "being in high school" and "GPA above 3.0" are not independent.