Talk:Chain Rule for Probability

So what's your point? --prime mover (talk) 22:09, 2 September 2022 (UTC)
 * I asked if this is mathematics. Do you really accept this proof? For me:
 * $\condprob A B = \dfrac {\map \Pr {A \cap B} } {\map \Pr B}$

is the definition, and what I read here is an informal justification e.g. for kids.


 * Why should we not cater for "kids", as you contemptuously call them? --prime mover (talk) 21:28, 3 September 2022 (UTC)


 * As much as I appreciate the work put down in writing this theorem, I have to agree with Usagiop. This is not a strict mathematical proof, it is a justification of a definition. My sources give:


 * 2001: Pierre Brémaud, Markov Chains, §2.2:
 * $\condprob A B \stackrel{ \mathrm{def} }{ = } \dfrac{ \map \Pr { A \cap B } }{ \map \Pr B }$


 * 2000: Michael Sørensen, En introduktion til sandsynlighedsregning, §1.4:
 *  The conditional probability of $B$ given $A$ ... is defined by:
 * $\condprob B A = \dfrac{ \map \Pr { A \cap B } }{ \map \Pr A }$


 * I think that Definition:Conditional Probability should be changed to give $\condprob A B = \dfrac{ \map \Pr { A \cap B } }{ \map \Pr B }$ as the definition. Then explan that the conditional probability is undefined when $\map \Pr B = 0$, for obvious reasons. --Anghel (talk) 12:16, 3 September 2022 (UTC)


 * Compromise. How about 2 definitions with an equivalence proof? --prime mover (talk) 21:29, 3 September 2022 (UTC)


 * Maybe we need to distinguish the modern probability theory (founded by Kolmogorov) from ancient probability theories like some in the greek mathematics. I guess, those definitions and proofs were accepted before the foundation of the modern probability theory.--Usagiop (talk) 17:35, 3 September 2022 (UTC)


 * Maybe is this style related to Cox's theorem?--Usagiop (talk) 18:49, 3 September 2022 (UTC)


 * As far as I know, the argument given here is pretty close to Kolmogorov's rationale for defining $\condprob A B$. It is not ancient theory, the sources given are from 1986, 1988 and 2014. But all sources I know of define $\condprob A B$ directly ( or accept is as an axiom of probability).
 * My earlier comment was perhaps too harsh. I still think Definition:Conditional Probability should be updated. Maybe we should give two definitions, one that accepts the definition as an axiom, and one that explains it like here. --Anghel (talk) 20:45, 3 September 2022 (UTC)