Online Encyclopedia
Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.
PROBABILITY (Lat. probabilis, probabl...
Online EncyclopediaEncyclopedia Home :: PRE-PYR
del.icio.us it!
|
See also:PROBABILITY (See also:Lat. probabilis, probable or credible) , a See also:term which in See also:general implies credibility See also:short of certainty. The mathematical theory of probabilities deals with certain phenomena which are employed to measure credibility. This Description measurement is well exemplified by See also:games of See also:chance. andDivision If a See also:pack of See also:cards is shuffled and a card dealt, the of the probability that the card will belong to a particular Subject. suit is measured by—we may say, is—the ratio 1:4, or I ; there being four suits to any one of them the card might have belonged. So the probability that an See also:ace will be See also:drawn is IA, as out of the 52 cards in the pack 4 are aces. So the probability that ace will turn up when a See also:die is thrown is e. The probability that one or other of the two events, ace or See also:deuce, will occur is I. If simultaneously a die is thrown and a card is dealt from a pack which has been shuffled, the probability that the See also:double event will consist of two aces is 1X4 divided by 6X52, as the See also:total number of double events formed by combining a See also:face of a die with a face of a card is 6X 52, and out of these I X4 consist of two aces. The data of probabilities are often prima facie at least of a type different from that which has been described. For example, the probability that a See also:child about to be See also:born will be a boy is about 0.51. This statement is founded solely on the observed fact that about 51 % of See also:children born (alive, in See also:European countries) prove to be boys. The probability is not, as in' the instance of See also:dice and cards, measured by the proportion between a number of cases favourable to the event and a total number of possible cases. Those instances indeed also admit of the measurement based on observed frequency. Thus the number of times that a die turns up ace is found by observation to be about 16.6% of the number of throws; and similar statements are true of cards and coins.' The probabilities with which the calculus deals admit generally of being measured by the number of times that the event is found by experience to occur, in See also:pro-portion to the number of times that it might possibly occur. The See also:idea of a probable or expected number is not confined to the number of times that an event occurs; if the occurrence of the event is associated with a certain amount of See also:money or any other measurable See also:article there will be a probable or expected amount of that article. For instance, if a See also:person throwing dice is to receive two shillings every See also:time that six turns up, he may expect in a See also:hundred throws to win about 2X 16.6 (about 33.3) shillings. If he is to receive two shillings for every six and one See also:shilling for every ace, his expectation will be 2 X 16.6+r X16.6 (5o) shillings. The expectation of lifetime is calculated on this principle. Of moo See also:males aged ten say the probable number who will die in their next See also:year is 490, in the following year 397, and so on; if we (roughly) estimate that those who die in the first year will have enjoyed one year of See also:life after ten, those who die in the next year will have enjoyed two years of life, and so on; 1 Cf. See also:note to See also:par. 5 below.PROBABILITY then the total number of years which the See also:I000 males 2 aged ten may be expected to live is I X 1000 + 2 X (1000—490) + 3 (1000—490—397) +.. . Space as well as time may be the subject of expectation. If drops of See also:rain fall in the See also:long run with equal frequency on one point—or rather on one small See also:interval, say of a centimetre or two—on a See also:band of finite length and negligible breadth, the distance which is to be expected between a point of impact in the upper See also:half of the See also:line and a point of impact in the See also:lower half has a definite proportion to the length of the given line.' Expectation in the general sense may be considered as a See also:kind of See also:average." The See also:doctrine of averages and of the deviations therefrom technically called "errors" is distinguished from the other portion of the calculus by the See also:peculiar difficulty of its method. The paths struck out by See also:Laplace and See also:Gauss have hardly yet been completed and made quite secure. The doctrine is also distinguished by the importance of its applications. The theory of errors enables the physicist so to combine discrepant observations as to obtain the best measurement. It may abridge the labour of the statistician by the use of samples.' It may assist the statistician in testing the validity of inductions.' It promises to be of See also:special service to him in perfecting the logical method of concomitant See also:variations; especially in investigating the See also:laws of See also:heredity. For instance the correlation between the height of parents and that of children is such that if we take a number of men all of the same height and observe the average height of their adult sons, the deviation of the latter average from the general average of adult males bears a definite proportion—about a half—to the similarly measured deviation of the height See also:common to the fathers. The same kind and amount of correlation between parents and children with respect to many other attributes besides stature has been ascertained by See also:Professor Karl See also:Pearson and his collaborators.' The See also:kinetics of See also:free molecules (gases) forms another important See also:branch of See also:science which involves the theory of errors. The description of the subject which has been given will explain the See also:division which it is proposed to adopt. In See also:Part I. probability and expectation will be considered apart from the peculiar difficulties incident to errors or deviation from averages. The first See also:section of the first part will be devoted to a preliminary inquiry into the See also:evidence of the See also:primary data and axioms of the science. Freed from philosophical difficulties the mathematical calculation of probabilities will proceed in the second section. The analogous calculation of expectation will follow in the third section. The contents of the first three sections will be illustrated in the See also:fourth by a class of examples dealing with space measurements—the so-called "See also:local" or "geometrical" probabilities. Part II. is devoted to averages and the deviations therefrom, or more generally that grouping of See also:statistics which may be called a See also:law of frequency. Part II. is divided into two sections distinguished by See also:differences in See also:character and extent between the See also:principal generalizations respecting laws of frequency. Additional information and CommentsThere are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML. Site content, images, and layout Copyright © 2006 - Net Industries, worldwide. |
|
|
[back] PROBABILISM (from Lat. probare, to test, approve) |
[next] PROBATE |