Conditional and joint probabilities of statistically dependent events

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SUMMARY

The discussion centers on the relationship between conditional probability and joint probability for statistically dependent events A and B. It is established that one can calculate joint probability if conditional probability is known, and vice versa. However, without knowledge of either probability, determining the independence of the events is impossible. This highlights the interdependence of these two concepts in probability theory.

PREREQUISITES
  • Understanding of conditional probability
  • Knowledge of joint probability
  • Familiarity with the concept of statistical dependence
  • Basic principles of probability theory
NEXT STEPS
  • Study the formulas for calculating conditional probability and joint probability
  • Explore examples of dependent and independent events in probability
  • Learn about Bayes' theorem and its applications
  • Investigate the implications of statistical dependence in real-world scenarios
USEFUL FOR

Students of statistics, data analysts, and professionals in fields requiring probabilistic modeling will benefit from this discussion.

PainterGuy
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Hi,

If the events A and B are statically dependent then the following formulas are used to calculate conditional probability and joint probability but there is a problem. As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first calculating joint probability, and one cannot calculate joint probability without knowing condition probability! Where am I going wrong? Could you please help me? Thank you!
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PainterGuy said:
As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first calculating joint probability, and one cannot calculate joint probability without knowing condition probability! Where am I going wrong? Could you please help me?
Well, you have to know something. If you know the conditional probability then you can calculate the joint probability. If you know the joint probability then you can calculate the conditional probability. If you don't know either then you cannot even tell if they are independent or not.
 
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