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

AI Thread Summary
P(A) represents the probability of event A occurring, while O(A) denotes the odds of event A occurring compared to it not occurring. The discussion highlights confusion around the notation O(A), particularly in relation to its definition in the context of Bayes' rule. It clarifies that O(A) is not explicitly defined in many resources, leading to misunderstandings. Ultimately, the distinction is that P(A) is based on the total outcomes, whereas O(A) compares the occurrence of A to its non-occurrence. Understanding these terms is crucial for grasping concepts in probability theory.
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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