# chance

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Related to chanced upon: To catch up

## probability

probability, in mathematics, assignment of a number as a measure of the “chance” that a given event will occur. There are certain important restrictions on such a probability measure. In any experiment there are certain possible outcomes; the set of all possible outcomes is called the sample space of the experiment. To each element of the sample space (i.e., to each possible outcome) is assigned a probability measure between 0 and 1 inclusive (0 is sometimes described as corresponding to impossibility, 1 to certainty). Furthermore, the sum of the probability measures in the sample space must be 1.

### Probability of Simple and Compound Events

A simple illustration of probability is given by the experiment of tossing a coin. The sample space consists of one of two outcomes—heads or tails. For a perfectly symmetrical coin, the likely assignment would be 1-2 for heads, 1-2 for tails. The probability measure of an event is sometimes defined as the ratio of the number of outcomes. Thus if weather records for July 1 over a period of 40 years show that the sun shone 32 out of 40 times on July 1, then one might assign a probability measure of 32/40 to the event that the sun shines on July 1.

Probability computed in this way is the basis of insurance calculations. If, out of a certain group of 1,000 persons who were 25 years old in 1900, 150 of them lived to be 65, then the ratio 150/1,000 is assigned as the probability that a 25-year-old person will live to be 65 (the probability of such a person's not living to be 65 is 850/1,000, since the sum of these two measures must be 1). Such a probability statement is of course true only for a group of people very similar to the original group. However, by basing such life-expectation figures on very large groups of people and by constantly revising the figures as new data are obtained, values can be found that will be valid for most large groups of people and under most conditions of life.

In addition to the probability of simple events, probabilities of compound events can be computed. If, for example, A and B represent two independent events, the probability that both A and B will occur is given by the product of their separate probabilities. The probability that either of the two events A and B will occur is given by the sum of their separate probabilities minus the probability that they will both occur. Thus if the probability that a certain man will live to be 70 is 0.5, and the probability that his wife will live to be 70 is 0.6, the probability that they will both live to be 70 is 0.5×0.6=0.3, and the probability that either the man or his wife will reach 70 is 0.5+0.6−0.3=0.8.

### Permutations and Combinations

In many probability problems, sophisticated counting techniques must be used; usually this involves determining the number of permutations or combinations. The number of permutations of a set is the number of different ways in which the elements of the set can be arranged (or ordered). A set of 5 books in a row can be arranged in 120 ways, or 5×4×3×2×1=5!=120 (the symbol 5!, denoting the product of the integers from 1 to 5, is called factorial 5). If, from the five books, only three at a time are used, then the number of permutations is 60, or In general the number of permutations of n things taken r at a time is given by On the other hand, the number of combinations of 3 books that can be selected from 5 books refers simply to the number of different selections without regard to order. The number in this case is 10: In general, the number of combinations of n things taken r at a time is

### Statistical Inference

The application of probability is fundamental to the building of statistical forms out of data derived from samples (see statistics). Such samples are chosen by predetermined and arbitrary selection of related variables and arbitrary selection of intervals for sampling; these establish the degree of freedom. Many courses are given in statistical method. Elementary probability considers only finite sample spaces; advanced probability by use of calculus studies infinite sample spaces. The theory of probability was first developed (c.1654) by Blaise Pascal, and its history since then involves the contributions of many of the world's great mathematicians.

### Bibliography

See P. Billingsley, Probability and Measure (1979); I. Hacking, The Emergence of Probability (1984, rev. ed. 2006); J. T. Baskin, Probability (1986); P. Bremaud, Introduction to Probability (1988); S. M. Ross, Introduction to Probability Theory (1989).

## chance

1. the PROBABILITYof an event, such as the occurrence of heads or tails on the toss of a coin.
2. social or physical outcomes which are unforseen and perhaps inherently unpredictable.
Chance arises from the existence of physical or social processes which involve random events, a multiplicity of interacting variables in ‘open systems’ (including the changeability of actors' choices), and because actors’ intentions often have UNANTICIPATED CONSEQUENCES. While an inherent CONTINGENCY in social events is seen by some theorists as ruling out general theories, this neglects the availability of generalized ‘probabilistic’ accounts and the fact that it is the goal of general theories to abstract from particular events (and provide EXPLANATION or analytical frameworks), not necessarily to predict or control events.

Coping with chance in social life is a source of MAGIC and RELIGION and the basis of important leisure forms, including games of chance and GAMBLING. See also RISK SOCIETY.

Collins Dictionary of Sociology, 3rd ed. © HarperCollins Publishers 2000

## Chance

Charity (See GENEROSITY.)
Bridoison, Taiel de
judge who casts dice to decide cases. [Fr. Lit.: Pantagruel]
Fata Morgana
lake-dwelling sorceress and personification of chance. [Ital. Lit.: Orlando Innamorato]
Fortuna
goddess of chance. [Rom. Myth.: Kravitz, 58]
Jimmy the Greek
renowned American oddsmaker. [Am. Culture: Wallechinsky, 468]
Russian roulette
suicidal gamble involving a six-shooter, loaded with one bullet. [Folklore: Payton, 590]
Sors
god of chance. [Rom. Myth.: Espy, 42–43]
Three Princes of Serendip
always make discoveries by accident. [Br. Lit.: Three Princes of Serendip]
Urim and Thummin
oracular gems used for casting lots, set in Aaron’s breastplate. [O.T.: Exodus 28:30; Leviticus 8:8]
References in classic literature ?
At rare intervals they chanced upon the trail of a snowshoe rabbit or an ermine; but in the main it seemed that all life had fled the land.
Then he chanced upon Kipling's poems, and was swept away by the lilt and swing and glamour with which familiar things had been invested.
Sometimes they chanced upon other wolves, usually in pairs; but there was no friendliness of intercourse displayed on either side, no gladness at meeting, no desire to return to the pack-formation.
We made great havoc in Touraine, until we came into Romorantin, where I chanced upon a gold chain and two bracelets of jasper, which were stolen from me the same day by a black-eyed wench from the Ardennes.
Nevertheless -- to hold nothing back from the reader -- it was because, on the third day from the present, he was to preach the Election Sermon; and, as such an occasion formed an honourable epoch in the life of a New England Clergyman, he could not have chanced upon a more suitable mode and time of terminating his professional career.
As I was about to lay the thing aside as of no value in my present predicament my eyes chanced upon a few strange characters roughly and freshly scratched upon the soft gold of the case.
John Michael dela Cruz chanced upon the unidentified man who snatched a bag of a jeepney passenger in Barangay Ilang-Ilang at about 7:45 p.m.
Solicitor Bruce Macdonald said: "Mr Wood was walking down Union Street and chanced upon a group of young people at a bus stop.
Kevin Lois Monsod was walking with his two male friends when they chanced upon the suspect on a motorcycle accompanied by three women at the corner of Concha and Quezon streets.
During the tour of the house, which has been preserved to its original state, Adnan chanced upon white and yellow cushion covers stamped with "100% cotton.
Upon reaching the area, they chanced upon more or less 10 fully armed NPAs.
Julieto Degorio were on a test mission when they chanced upon the communist reb-els who were having a plenum in Sitio Calogtogan, Barangay Anislagan.

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