What does division mean in probability? If I understand correctly,

>>8058839
>If I understand correctly
you don't

>>8058839
I always think of it as disregarding redundant cases.

>>8058839
>A 'if' B.

If you don't understand it just apply whatever variables you have to Bayes's theorem and it'll work.

A subset

>>8058839
The vertical line denotes a conditional circumstance, so the left side of the equation, translated, means the probability of A given B.

It is for re-evaluating the probability of a hypothesis given new evidence after the probability is determined once.

>>8059047
...but I'm talking about the horizontal line.

>>8058839
You're just renormalizing because you're restricting to a smaller probability space. There's some shit data analysis textbook that uses Bayes all over without the denominator, and replaces every equality with a proportIon. Because the constant is just to give you back a proper distribution

>>8059061
In the picture of that formula, the bottom is the new, smaller sample space, and the top is the stuff you care about happening out of the smaller sample space.

>>8058839
Dividing in probability is a little like dividing areas, getting ratios in relation to a venn diagram

>>8058839
Why would anyone want Baye's Theorem in neon?

>>8060013
To make it more visible.

>>8058839
First of all [probability (A union B)] is equal to P(A) + P(B) - P(A intersection B).

As for P(A)/P(B) it only makes sense if A is a subset of B and then it would mean [probability A given B] = P(A)/P(B).

>>8059066
Most coherent naive formulation yet. When you start integrating things become very fuzzy. The good news is that it all works out except when it doesn't. And if you restrict yourself to convenient optimization you can get a lucrative job PROVING things management wants to hear. Good times.

>>8058839
P(A)/P(B) is the chance of A given B, if A is a subset of B

bimp

>>8060028
>>8060090
>As for P(A)/P(B) it only makes sense if A is a subset of B
>P(A)/P(B) is the chance of A given B
...or it could just represent some odds.

>>8058839
Conditional probability, anon.
P[A|B] denotes the probability of A occurring, provided that B has already occurred. Solving problems based on Bayes' theorem helps a lot when it comes to understanding conditional probability.

OP, there's an answer to your question but it requires understanding some analysis, basically just measure theory.

https://en.wikipedia.org/wiki/Probability_theory#Measure-theoretic_probability_theory


Modern probability is all measure theory.

Otherwise what you're asking is just about dividing numbers. P(anything) is just a number. So you can divide them. We sometimes think of this division in terms of subsets, as you could do with any numbers and as some people have pointed out above. Nothing unusual.