If you know the probability of an event occurring how do you express the odds for or against? There seems to be a lot of confusion around this question and even I have misstepped when it comes to correctly handling odds.

There is a simple formula.

If there is a probability p of an event happening then the odds in favor of the event are p /(1 − p).

To find the odds against, take the reciprocal: (1 − p)/p

Another way to express this is:

1. The odds in favor of an event are just the ratio of the probability that the event happens to the probability that it won't happen.

2. The odds against an event are just the reciprocal of the odds in favor.


EXAMPLE

Suppose you have a fair 6-sided die and you're interested in the event of rolling a 4 in a single roll.


The probability of this event happening is p = 1/6

The probability of it not happening is 1 - p = q = 5/6


The odds in favor of rolling a 4 are p/q = 1/5

commonly written 1:5 and pronounced "1 to 5"

The odds against rolling a 4 are q/p = 5/1

commonly written 5:1 and pronounced "5 to 1"

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.