Please explain in simple terms so that i can start practice on this area.
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%.
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%
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).
excuse me, I am a little confused about ‘odds’, ‘odds against’ and ‘probability’. could you please interpret by taking some examples?
And I`m also puzzled about the content from the note that ‘Consider an event that has a probability of occurrence of 0.125, which is one-eighth. the odds that the event will occur are 1/7, which we state as “the odds for the event occurring are one-to-seven”.’
I don’t know the reason why the chances of occurrence for the event is 1/7, rather than 1/(1+8). Could you please explain that for me?
Odds represent the payoff on a fair bet; i.e., a bet whose expected value is zero.
If the probability of something occurring (say, a particular horse winning a race), is 0.125 (= 1/8). The (fair) odds against that horse winning would be posted as 7:1. (Note that the real odds posted will be something less: the track always cheats the bettors.) If the race were run eight times and that horse won once (as expected), a bettor would lose $1 seven times and win $7 once, for an net payoff of zero.
Thank you very much. Your answer helps me so much.
My pleasure.