# Probability

## Odds

Odds are a way to express the likelihood of an event taking place. For instance, what are the odds of Seabiscuit winning this horse race? They’re often written X to Y or X:Y, or X/Y.

In gambling, you use odds as in odds of not happening. 10:1 odds mean you bet 1 dollar, and if you win, you get 10 dollar + your original 1 dollar.

In usual odds you say 2:1 which means the event is twice as likely to occur than not, hence you bet $2 and only get $1.

Odds are a ratio: \(\frac{Probability The Event Happens}{Probability The Event Does NOT Happen} = \frac{p}{1-p}\)

$ Odds = \frac {probability} {1 - probability} = \frac {Events Happening / Subjects} {Events Note Happening / Subjects}$

or

$ Probability = \frac {odds}{1+odds}$