Say we have two events, $~$A$~$ and $~$B$~$, and a probability distribution $~$\\bP$~$ over whether or not they happen\. We can represent $~$\\bP$~$ as a square:

Does this actually work for any proportions of A and B? Is there a simple proof?

by Eric Rogstad Jun 16 2016

Say we have two events, $~$A$~$ and $~$B$~$, and a probability distribution $~$\\bP$~$ over whether or not they happen\. We can represent $~$\\bP$~$ as a square:

Does this actually work for any proportions of A and B? Is there a simple proof?

## Comments

Eric Rogstad

And is there any significance to the fact that A and -A are divided by a straight line, but B and -B are divided by a jagged line? Could we have arranged the rectangle so that B and -B were divided by a straight line w/o changing any of the probabilities?

Tsvi BT

Yes, but I'm not sure it's worth proving? I'd say that the "Factoring" section explains how this works, though there are no proofs. Will add pointers at the beginning.

This is addressed in the factoring section.