What is the difference between P(A) and O(A)?

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SUMMARY

P(A) represents the probability of event A occurring, calculated as the number of favorable outcomes divided by the total number of outcomes. O(A), on the other hand, denotes the odds of event A occurring compared to the odds of it not occurring. This distinction is crucial in probability theory, particularly in contexts such as Bayes' rule, where understanding both concepts enhances comprehension of statistical models and decision-making processes.

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  • Basic understanding of probability theory
  • Familiarity with Bayes' rule
  • Knowledge of odds versus probability concepts
  • Ability to interpret statistical equations
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  • Study the derivation of Bayes' rule in detail
  • Learn how to convert probabilities to odds and vice versa
  • Explore advanced probability concepts such as conditional probability
  • Investigate real-world applications of odds in decision-making
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Students of statistics, data analysts, and professionals in fields requiring probabilistic reasoning will benefit from this discussion, particularly those looking to deepen their understanding of probability and odds in statistical contexts.

CaseyJRichard
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In probability, P(A) is the probability of event A occurring.

What is O(A), in the same context? I've tried looking this up, but I can't find the definition/explanation of this notation anywhere.

For an example, see the definition of "Bayes' rule".
 
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Do you mean the definition at Wikipedia? It defines O in the fourth equation under "Derivation".
 
It's not really defining O there, is it? It's defining an equation that uses O, sure, but it still doesn't explain what the notation "O" represents. But maybe I just don't understand the equation.

Regardless, the answer I was looking for is:

O(A) is the "Odds" of event A occurring (versus event A not occurring), whereas P(A) is the "Probability" of event A occurring. (i.e., the number of outcomes where A occurs over the total number of outcomes.)
 

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