Urgent Help involving Odds!

Question

Could someone explain what the odds against and the odds in favor mean? I'm still a little confused, as well as when it is stated for example, the odds in favor of winning an election are 2 to 5 or there is a 4 to 5 chance that it is going to rain, I'm confused with numbers like if its supposed to be a good chance or not.

I was given a task where I have to come up with a question involving odds, I wanted to create a question stating what are the odds/chances of finding the lost treasure in a forest, what would I say? (In this case, it is easy to find the treasure) so the chances are a lot bigger, I just wanted the numbers to be accurate.

Answer 1

Hi Sam,

Here’s how odds and probability are related:

a Probability is a number between 0 and 1, where 1 means “certain” and 0 means “impossible”

if p is probability of the event, the odds in favor are p / (1-p)

so if p = .2, then

odds in favor are .2/.8 = 1 to 4, and

odds against are .8/.2 = 4 to 1. You see that

(in favor) = 1 / (against) and

(against) = 1 / (in favor)

another example:

if p = .7, then

odds in favor are .7 / .3 = 2.3 to 1 and

odds against are .3 / .7 = .43 to 1

if the odds are M to N, which means M / N,

p = M/(M+N)

So in the first example

if odds in favor are 1 to 4, p = 1 / (1+4) = .2

and odds against are 4 to 1, p = 4/(1+4) = .8

similarly

if odds in favor are 2.3 to 1, p = 2.3/3.3= .7

and odds against are .43 to 1, p =.43/1.43 = .3

yet another example, when people say there are “even odds” or “equal odds”, they are saying the odds are 1 to 1.

so the formula says

p = 1/(1+1) = 1/2 = .5

I hope this helps. If not, please ask another question.

Heres the derivation, if you’re interested:

odds = ( p / (1-p) )

odds * (1-p) = p

odds - p*odds = p

M / N - p*M/N = p

solving for p

M/N = p ( 1 + M/N )

p = (M/N) / (1+M/N)

p =(M/N) / ((N+M)/N) = MN / N(M+N) = M/(M+N)