Are GPA and Skipped Classes Related Through Conditional Probabilities?

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SUMMARY

The discussion centers on the relationship between GPA and class attendance, specifically analyzing conditional probabilities. It presents data showing that among students with a GPA between 2 and 3, 450 skipped few classes, while 25 skipped many classes. The conclusion drawn is that GPA between 2 and 3 and skipping few classes are not independent events, as evidenced by the calculations showing that P(A n B) does not equal P(A) * P(B). The correct answer to the posed question is A, as the probabilities do not align.

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  • Understanding of conditional probability
  • Familiarity with GPA grading systems
  • Basic knowledge of statistical independence
  • Ability to interpret probability equations
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  • Study the concept of conditional independence in probability theory
  • Learn how to calculate joint probabilities using the product rule
  • Explore statistical methods for analyzing GPA trends in educational research
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Students, educators, and researchers interested in the correlation between academic performance and attendance patterns, particularly in the context of statistical analysis and educational outcomes.

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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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