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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).
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%).
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position.
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 .
The mathematical tools for making predictions about what measurement outcomes may occur, and how quantum states can change, were developed during the 20th century and make use of linear algebra and functional analysis. Quantum physics has proven to be an empirical success and to have wide-ranging applicability.
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
A subset of the sample space of a procedure or experiment (i.e. a possible outcome) to which a probability can be assigned. For example, on rolling a die, "getting a three" is an event (with a probability of 1 ⁄ 6 if the die is fair), as is "getting a five or a six" (with a probability of 1 ⁄ 3).
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]