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"odds" Deutsch ÜbersetzungÜbersetzung für 'odds' im kostenlosen Englisch-Deutsch Wörterbuch von LANGENSCHEIDT – mit Beispielen, Synonymen und Aussprache. Übersetzung von odds – Englisch–Deutsch Wörterbuch. odds. noun plural. ○. chances; probability. die Chance. The odds are that he will win. Viele übersetzte Beispielsätze mit "odds" – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen.
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When gambling, odds are often the ratio of winnings to the stake and you also get your wager returned. If you make 6 wagers of 1, and win once and lose 5 times, you will be paid 6 and finish square.
These example may be displayed in many different forms:. The language of odds, such as the use of phrases like "ten to one" for intuitively estimated risks, is found in the sixteenth century, well before the development of probability theory.
The sixteenth-century polymath Cardano demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes.
Implied by this definition is the fact that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes.
In statistics, odds are an expression of relative probabilities, generally quoted as the odds in favor. The odds in favor of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen.
Mathematically, this is a Bernoulli trial , as it has exactly two outcomes. In case of a finite sample space of equally likely outcomes , this is the ratio of the number of outcomes where the event occurs to the number of outcomes where the event does not occur; these can be represented as W and L for Wins and Losses or S and F for Success and Failure.
For example, the odds that a randomly chosen day of the week is a weekend are two to five , as days of the week form a sample space of seven outcomes, and the event occurs for two of the outcomes Saturday and Sunday , and not for the other five.
For example, the odds against a random day of the week being a weekend are Odds and probability can be expressed in prose via the prepositions to and in: "odds of so many to so many on or against [some event]" refers to odds — the ratio of numbers of equally likely outcomes in favor and against or vice versa ; "chances of so many [outcomes], in so many [outcomes]" refers to probability — the number of equally like outcomes in favour relative to the number for and against combined.
For example, "odds of a weekend are 2 to 5", while "chances of a weekend are 2 in 7". In casual use, the words odds and chances or chance are often used interchangeably to vaguely indicate some measure of odds or probability, though the intended meaning can be deduced by noting whether the preposition between the two numbers is to or in.
Odds can be expressed as a ratio of two numbers, in which case it is not unique — scaling both terms by the same factor does not change the proportions: odds and odds are the same even odds.
Odds can also be expressed as a number, by dividing the terms in the ratio — in this case it is unique different fractions can represent the same rational number.
Odds as a ratio, odds as a number, and probability also a number are related by simple formulas, and similarly odds in favor and odds against, and probability of success and probability of failure have simple relations.
Analogously, given odds as a ratio, the probability of success or failure can be computed by dividing, and the probability of success and probability of failure sum to unity one , as they are the only possible outcomes.
In case of a finite number of equally likely outcomes, this can be interpreted as the number of outcomes where the event occurs divided by the total number of events:.
This is a minor difference if the probability is small close to zero, or "long odds" , but is a major difference if the probability is large close to one.
These transforms have certain special geometric properties: the conversions between odds for and odds against resp. They are thus specified by three points sharply 3-transitive.
Swapping odds for and odds against swaps 0 and infinity, fixing 1, while swapping probability of success with probability of failure swaps 0 and 1, fixing.
Converting odds to probability fixes 0, sends infinity to 1, and sends 1 to. In probability theory and statistics, odds and similar ratios may be more natural or more convenient than probabilities.
In some cases the log-odds are used, which is the logit of the probability. Most simply, odds are frequently multiplied or divided, and log converts multiplication to addition and division to subtractions.
This is particularly important in the logistic model , in which the log-odds of the target variable are a linear combination of the observed variables.