I Conditional and joint probabilities of statistically dependent events

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In the discussion about conditional and joint probabilities of statistically dependent events, it is highlighted that both types of probabilities are interdependent. Conditional probability can be calculated if joint probability is known, and vice versa. However, without knowledge of either probability, one cannot determine the independence of the events. The confusion arises from the assumption that both probabilities must be calculated simultaneously. Understanding the relationship between these probabilities is crucial for accurate statistical analysis.
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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