How to get the probability of an event from odds.

[stuartbale1]

Please explain in simple terms so that i can start practice on this area.

 

[S2000magician]

If the (a priori) odds against the Broncos winning yesterday’s Super Bowl were 8:5, then the (a priori) probability of the Broncos losing would be 8 / (8 + 5) = 61.54%, and the (a priori) probability of the Broncos winning would be 5 / (8 + 5) = 38.46%.

 

[JSD - NYC]

Odds are an ugly and generally unhelpful way to think about probability, but it may come up. Think of each side of the ratio as the number of possibilities out of all possible possibilities of the event happening or not happening.
Start with something easy:
1:1 odds would tell us there is a 50%-50% chance of the event happening. 1 chance that it happens and 1 change it doesn’t happen.
Go to something a little harder:
1:2 odds is 1 chance the event will happen and 2 chances it won’t or 33% probability.
You can also reverse it:
2:1 odds means 66% chance the event happens.
So, keep the easy examples in mind, then you can go to the generalized formula:
A:B odds means A chances of the event happening and B chances that it wont. That means there are A+B total chances between the event happening or not happening. To get the proabability that the event happens, just take A / (A+B).
So, no matter how big or difficult the numbers get, just go back to the simple formula and the easy examples to sort yourself out:
111111:222222 = 111111/(111111+222222) = 111111/333333= 33.33%

 

[S2000magician]

JSD - NYC wrote:Start with something easy:
1:1 odds would tell us there is a 50%-50% chance of the event happening. 1 chance that it happens and 1 change it doesn’t happen.
Go to something a little harder:
1:2 odds is 1 chance the event will happen and 2 chances it won’t or 33% probability.
You can also reverse it:
2:1 odds means 66% chance the event happens.

Bear in mind that you’re writing the odds in favor of an event happening.
Most people’s experience with odds is with the odds against an event happening. For example, the odds given in a horse race are the odds against each horse winning (or placing, or showing).