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In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. [2]
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.
These definitions are equivalent, since dividing both terms in the ratio by the number of outcomes yields the probabilities: : = (/): (/). Conversely, the odds against is the opposite ratio. For example, the odds against a random day of the week being during a weekend are 5:2.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
The outcomes must be collectively exhaustive, i.e. on every experiment (or random trial) there will always take place some outcome for {,, …,}. [ 6 ] The sample space ( Ω {\displaystyle \Omega } ) must have the right granularity depending on what the experimenter is interested in. Irrelevant information must be removed from the sample space ...
The classical definition of probability assigns equal probabilities to events based on physical symmetry which is natural for coins, cards and dice. Some mathematicians object that the definition is circular. [11] The probability for a "fair" coin is... A "fair" coin is defined by a probability of... The definition is very limited.
The classical definition of probability works well for situations with only a finite number of equally-likely outcomes. This can be represented mathematically as follows: If a random experiment can result in N mutually exclusive and equally likely outcomes and if N A of these outcomes result in the occurrence of the event A , the probability of ...