MHB Multiplication Theorem on Probability and proof

AI Thread Summary
The discussion centers on the Multiplication Theorem in probability, specifically regarding the simplification of conditional probabilities. A user expresses confusion about the theorem and seeks clarification on how the simplification works and its importance. Another participant explains that the simplification is based on the standard rules of fraction multiplication and cancellation. The example provided illustrates how terms can be canceled in a multiplication of fractions. Understanding this simplification is crucial for grasping the theorem's application in probability.
alfred2
Messages
8
Reaction score
0
Hi Everyone!

I'm with Conditional Probability and I don't understan this theorem.

Theorem:
If
http://imageshack.us/a/img28/1349/1qg.png
then
http://imageshack.us/a/img209/8829/aor.png
Proof:
All the conditional probabilities are well defined, since
http://imageshack.us/a/img197/8938/4xp.png
We can rewrite the right site of the equality as follows
http://imageshack.us/a/img62/3095/5d9.png
Obviously we can simplify the terms through
http://imageshack.us/a/img855/7523/ikm.png
Can anyone say me how does the simplification work? And why it is so important to be sure that

Thank you =)
 
Mathematics news on Phys.org
Welcome to MHB, alfred! :)

The simplification is a consequence of how fractions are multiplied and simplified in general.
Consider for instance:
$$\frac 3 4 \cdot \frac 4 5 \cdot \frac 5 6 = \frac 3 {\cancel 4} \cdot \frac {\cancel 4} {\cancel 5} \cdot \frac {\cancel 5} 6 = \frac 3 6$$
 
Thanks! You were right ;)
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top