# Odds

Odds are a tool for ex­press­ing rel­a­tive chances. If the odds of a tree in a for­est be­ing sick ver­sus healthy are 2 : 3, this says that there are 2 sick trees for ev­ery 3 healthy trees. (The prob­a­bil­ity of a tree be­ing sick, in this case, is 25 or 40%.)

Odds are ex­pressed in the form “X to Y”, e.g. “7 to 9 for X ver­sus Y”, more com­pactly writ­ten as $$7:9$$.

The rep­re­sen­ta­tion of chances as odds is of­ten used in gam­bling and statis­tics.

Children:

• Odds: Introduction

What’s the differ­ence be­tween prob­a­bil­ities and odds? Why is a 20% prob­a­bil­ity of suc­cess equiv­a­lent to 1 : 4 odds fa­vor­ing suc­cess?

• Odds: Refresher

A quick re­view of the no­ta­tions and math­e­mat­i­cal be­hav­iors for odds (e.g. odds of 1 : 2 for draw­ing a red ball vs. green ball from a bar­rel).

• Odds: Technical explanation

For­mal defi­ni­tions, al­ter­nate rep­re­sen­ta­tions, and uses of odds and odds ra­tios (like a 1 : 2 chance of draw­ing a red ball vs. green ball from a bar­rel).

Parents:

• Probability theory

The logic of sci­ence; co­her­ence re­la­tions on quan­ti­ta­tive de­grees of be­lief.

• One as­pect I find a bit con­fus­ing in this ex­pla­na­tion: the differ­ence be­tween the no­ta­tions “3 /​ 2” and “3 : 2″. In my mind, both cor­re­spond to “one and a half”. But then sud­denly I run into 3:2:6 and get pretty con­fused.

How­ever, af­ter in­ves­ti­gat­ing a bit, the us­age of the colon ( : ) for di­vi­sion is com­mon in France (I stud­ied most of my Maths in France), but not in English-speak­ing coun­tries, where /​ and ÷ are used in­stead (we would write “3 : 2 = 1,5”). So when you peo­ple use “:” you’re not talk­ing about di­vi­sion at all, but only ra­tios, so it makes sense.

I’m not sure this war­rants spe­cial ex­tra ex­pla­na­tions un­less other peo­ple get con­fused by the same thing (Ap­par­ently Ger­mans use the colon for di­vi­sion too).