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

In summary, P(A) represents the probability of event A occurring, while O(A) represents the odds of event A occurring versus not occurring. These two notations are often used in probability and can be seen in the definition of Bayes' rule on Wikipedia.
  • #1
CaseyJRichard
4
0
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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  • #2
Do you mean the definition at Wikipedia? It defines O in the fourth equation under "Derivation".
 
  • #3
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.)
 

1. What is probability notation?

Probability notation is a way of representing the likelihood or chance of an event occurring. It is typically represented by a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. It is often denoted by the letter P.

2. What are the different types of probability notation?

There are several types of probability notation, including conditional probability (P(A|B)), joint probability (P(A and B)), and marginal probability (P(A)). Each type represents a different aspect of probability, such as the probability of an event occurring given another event has already occurred, the probability of two events occurring together, and the probability of a single event occurring.

3. How is probability notation used in statistical analysis?

In statistical analysis, probability notation is used to calculate the likelihood of certain outcomes based on available data. It allows scientists to make predictions and draw conclusions about a population based on a sample of data.

4. Can probability notation be used to make predictions about future events?

Yes, probability notation can be used to make predictions about future events. By analyzing past data and calculating the probability of certain outcomes, scientists can make informed predictions about future events.

5. How can I improve my understanding of probability notation?

To improve your understanding of probability notation, it is helpful to practice solving problems and working with different types of notation. There are also many online resources and textbooks available that provide explanations and examples of probability notation in action.

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