Help Understanding something basic in probability.

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Division in probability, represented as A/B, can refer to different concepts depending on context. It may represent the division of probabilities as real numbers, particularly in conditional probabilities and Bayesian analysis, but the result is not always a valid probability. The expression A|B denotes the probability of event A occurring given that event B has occurred, which is not arithmetic division. Additionally, A/B can also refer to the ratio of two random variables, which can be complex if either variable can be zero. Understanding the specific context is crucial for accurately interpreting the meaning of division in probability.
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Can somebody explain to be in detail what division represents in probability. Like A/B. I know it sounds very basic, but I just don't understand it. The events and all.
 
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Archive said:
Can somebody explain to be in detail what division represents in probability. Like A/B. I know it sounds very basic, but I just don't understand it. The events and all.

I don't know how much detail you want. You can divide probabilities like any other numbers, but the result will not always be a probability (see likelihood). Formulas where division of probabilities are utilized are so constructed such that if the result is a probability, the values will always be 0< p< 1. (see Bayes Theorem). Beyond this, I can't give you general answer as to what the division of probabilities "represents". It depends on the context.
 
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I think you need to be much more specific with your question. Division is just division, in probability or anything else. Maybe you're referring to http://en.wikipedia.org/wiki/Odds" ?
 
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Welcome to PF!

Hi Archive! Welcome to PF! :wink:
Archive said:
Can somebody explain to be in detail what division represents in probability. Like A/B.

Do you mean A|B?

That's "the probability of A happening, given that B has happened" …

but it isn't division, in fact it isn't arithmetic at all. :smile:
 
I can think of:

1. division of probabilities as real numbers. This is associated with but not confined to conditional probabilities and Bayesian analysis, as noted above.
2. ratio of two random variables. For example you may be asked to derive the distribution of A/B, where each of A and B are random variables. This can be tricky; for example if the domains of both A and B include 0 then with some probability (> 0) the value of A/B will be indeterminate.
 
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Hmmm, if it's not anything that anyone else has already suggested maybe you're referring to the difference (A\B) between sets A and B.

If that's the case, then it's not really division but more like subtraction with A\B being the set of all outcomes in A that are not in B, i.e. A ∖ B = A ∩ Bc (Bc being the complement of B). So if you were drawing out a Venn diagram of that, A \ B would be everything in the A circle except for where the A circle intersects the B circle.
 
I got it thanks guys, sorry for the vague question.
 

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