[[Probabilità]] theory mathematically formulates incomplete knowledge pertaining to the likelihood of an occurrence.
For example, a meteorologist might say there is a 60% chance that it will rain tomorrow. This means that in 6 of every 10 times when the world is in the current state, it will rain.
A '' probability'' is a real number <math>p \in [0,1]</math>. In everyday speech, the number is usually expressed as a percentage ( between 0% and 100%) rather than a decimal ( i.e., a probability of 0 .25 is expressed as 25%). A probability of 100% means that an event is certain. In everyday speech, probability of 0% is taken to mean that the event is impossible, but ( usually in where there are an infinity of possible outcomes) an event originally ascribed a probability of 0% MAY be the one that occurs. In some situations, it is CERTAIN that the event which occurs will be one that originally was ascribed zero probability ( for example, in selecting a number uniformly between 0 and 1, the probability of selecting any given number is zero, but it is certain that one such number will be selected).
Another way of referring to probability of an outcome is by its ''odds'': the ratio of the probability of "success" (event occurs) to the probability of "failure" (event does not occur). In the gambling world (where "odds" evolved) odds are expressed as the ratio of the STAKES risked by each participant in a wager. For instance: a bookmaker offering odds of 3/1 "against" a horse will pay a punter three times their stake (if the horse wins). In fact, the bookmaker (ignoring factors such as his potential need to "lay off" bets which are exposing him to the possibility of an unacceptable overall loss) is announcing that he thinks the horse has a 1/4 chance of winning. Using the mathematical definition of odds, "chance of winning" : " chance of not winning" = 1/4 : 3/4 = 1:3 or 1/3. So an event with a probability of 25% has odds of 33%. This disparity is even more clear where an event has a probability of 50% (e.g., the ODDS of a coin showing heads is 50%:50% = 1:1 or 1).
==Tipi di probabilità==