Are GPA and Skipped Classes Related Through Conditional Probabilities?

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The discussion centers on the relationship between GPA and class attendance, specifically analyzing whether the two variables are independent through conditional probabilities. Data shows that a significant number of students with a GPA below 2 have skipped many classes, while those with higher GPAs tend to skip fewer classes. The calculations reveal that the probabilities do not align, indicating a dependence between GPA and class attendance. Participants confirm that the independence condition, P(A n B) = P(A) * P(B), is not satisfied in this case. The conclusion drawn is that GPA and skipped classes are related, contradicting the notion of independence.
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Many skipped classes: GPA < 2 = 80 people, GPA between 2 and 3 = 25 people, GPA > 3 = 5 people

Few skipped classes: GPA < 2 = 175 people, GPA between 2 and 3 = 450 people, GPA > 3 = 265

Are "GPA between 2 and 3" and "skipped few classes" independent?
A. No, b/c .475 does not equal .506
B. No, b/c .475 does not equal .89
C. No, b/c .450 does not equal .475
D. Yes, because of conditional probabilities
E. Yes, because of the product rule

I know that they are independent if P(A n B) = P(A) * P(B)
.45 = .475 * .89
No it does not, .45 does not equal .42275
 
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