“probability”的概念、定义、翻译、参考文献-科学参考

probability

Physics

The likelihood of a particular event occurring. If there are n equally likely outcomes of some experiment, and a ways in which event E could occur, then the probability of event E is a/n. For instance, if a die is thrown there are 6 possible outcomes and 3 ways in which an odd number may occur. The probability of throwing an odd number is 3/6=1/2.

Mathematics

The probability of an event A, denoted by Pr(A), is a measure of the possibility of the event occurring as the result of an experiment. For any event A, 0 ≤ Pr(A) ≤ 1. If A never occurs, then Pr(A) = 0; if A always occurs, then Pr(A) = 1. If an experiment is repeated n times and the event A occurs m times, then the limit of m/n as n → ∞ is equal to Pr(A).

If the sample space S is finite and the possible outcomes are all equally likely, then the probability of the event A equals |A|/|S| (where | | denotes cardinality). The probability that a randomly selected element from a finite population belongs to a certain category is equal to the proportion of the population belonging to that category.

The probability that a discrete random variable X takes the value x_i is denoted by Pr(X = x_i) (see probability mass function). The probability that a continuous random variable X takes a value less than or equal to x is denoted by Pr(X ≤ x) (see cumulative distribution function).

The term ‘probability’ also refers generally to the theory of probability and stochastic processes and is intimately linked with statistics.

See also conditional probability, laws of large numbers, prior probability, probability density function, probability space.

Statistics

The probability of an event (see sample space) is a number lying in the interval 0≤p≤1, with 0 corresponding to an event that never occurs and 1 to an event that is certain to occur. For an experiment with N equally likely outcomes the probability of an event A is n/N, where n is the number of outcomes in which the event A occurs. For some experiments, such as throwing a drawing pin and seeing whether it lands point up, there is no possible set of equally likely outcomes. In the ‘frequentist’ view of probability, the probability of getting ‘point up’ is the limit, in some sense, of the relative frequency as the number of experiments tends to infinity. In the context of Bayesian inference, each observer has his or her own a priori distribution for the probability, which is then modified a posteriori in the light of whatever results have been obtained. Laplace claimed that ‘probability theory is nothing but common sense reduced to calculation’.

Chemical Engineering

The statistical likelihood of an event or a sequence of events occurring during a defined interval of time, or the chances of a success or failure of an event. It is used in quality control, risk assessment, and also to determine the reliability of process equipment and operations (see fmea). The probability of something happening or not happening is expressed as a dimensionless number ranging from 0 and 1. For example, if there are m possible outcomes and n ways an event can occur, then there is a probability of n/m chances of an occurrence. If the probability of success of a pump operating is S, then the probability of pump failure is F = 1−S. For example, if a process operates with three pumps, A, B, and C, each with equal chances of success in operating, then the possible combination of success and failure for the pumps is:

Pump

A

B

C

Probability

S

S

S

S³

S

S

F

S²F

S

F

S

S²F

S

F

F

SF²

F

S

S

S²F

F

F

S

SF²

F

S

F

SF²

F

F

F

F³

The sum of the probabilities is:
$S^{3} + 3 S^{2} F + 3 S F^{2} + F^{3} = {(S + F)}^{3}$

If there is an equal chance of each pump functioning being 1 in 10, say, then the probability of at least one pump being functional is:
$S^{3} + 3 S^{2} F + 3 S F^{2} = {0.9}^{3} + 3 \times {0.9}^{2} \times 0.1 + 3 \times 0.9 \times {0.1}^{2} = 0.999$

whereas the chance of at least two pumps being functional is:
$S^{3} + 3 S^{2} F = {0.9}^{3} + 3 \times {0.9}^{2} \times 0.1 = 0.972.$

The probability of failure on demand is therefore the likelihood that a process, system, or item of process plant will fail to operate in the required and expected manner on demand.

Computer

A number between 0 and 1 associated with an event (see relative frequency) that is one of a set of possible events: an event that is certain to occur has probability 1. The probability of an event is the limiting value approached by the relative frequency of the event as the number of observations is increased indefinitely. Alternatively it is the degree of belief that the event will occur.
The concept of probability is applied to a wide range of events in different contexts. Originally interest was in the study of games of chance, where correct knowledge of probability values allowed profitable wagers to be made. Later the subject was studied by insurance companies anxious to predict probable future claims on the basis of previously observed relative frequencies. Today probability theory is the basis of statistical analysis (see statistical methods).
The probability calculus is the set of rules for combining probabilities for combinations of events, using the methods of symbolic logic applied to sets.
See also probability distributions.