Difference Between Odds and Probability

Odds vs Probability

Probability is a mathematical assumption of chance that can be calculated using an equation. The equation measures the chances for an event to occur against the total number of chances that occurrence may produce. That is:

(Chances for)(Total Chances)

Odds, on the other hand, are a measure of chance that cannot be mathematically calculated, per se. The odds of a particular event occurring is more a measure of chances for the event happening to the chances of the occurrence not happening –that is, (chances for) : (chances against). If one is to consider total chances as (chances for) + (chances against), then an equation may be ascertained to mathematically calculate the odds of an event occurring:

Chances against=Total Chances- (Chances for)
and vice-versa:

Chances for=Total Chances- (Chances against)

The main consideration as regards odds is that they do, in fact, depend on probability. Though it is not a definite fact that the two are completely different in concept, in construction, one calculates odds using probability theory or statistics. In such a case, there is a straightforward equation to finding out what odds are in favour (or against) an event occurring. Consider p as probability:

Odds for=p1-p
and vice-versa:

Odds against=(1-p)p

Probability, on the other hand, measures the totality of an event occurring in a total number of events; therefore, the concern does not lie on if an occurrence will happen, but how often an event will occur. For example, when calculating how often one may draw a heart out of a deck of cards, one takes into consideration how many hearts are in a traditional deck of 52 cards:

Number of HeartsNumber of Cards=1352=14

If one is trying to calculate the odds for getting a heart in a deck of 52 cards, he will have to consider the probability that he will draw a heart from the deck:

Odds for=.25(1-.25)=.25.75=13
That means that the odds are 1 to 3 that a heart will be drawn from a traditional deck of 52 cards.

Summary:
1. Probability is a mathematical measure of how often an event will occur; odds are based on the probability that an event will ever occur
2. Probability only measures the chances that an event will occur against the total number of times the even will occur; odds measure the chances for and the chances against an event ever occurring.
3. Probability ensures that an event will occur; odds is used to find out if an event will ever occur.

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