Boy .513, girl .487. Although symmetry?

Symmetry.

Simulation.

Probability that Stanford will beat Cal?

or **What are the odds?**.

If you know about betting, you may believe for instance that it is much more likely that Stanford will win, you might accept a ``2 to 1'' odds bet, ie you pay 2 dollars if Stanford wins and you receive 1 dollar if they win. You think the probability of winning is 2/3.

*r* to 1 odds means that *E* occurs?
This means you beleive it is *r* times more likely that
*E* occurs than not.

So that .

If we generalise this to an event *E* whose odds are
*r* to *s*, written (*r*:*s*), then

If *P*(*E*)=*p* then the odds in favor of *E* are:
*r*:*s* where
*r*/*s*=*p*/(1-*p*).

An extension to property 3 to 3 events is done by
writing:

Inclusion-Exclusion Principle for