probability

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The quality or condition of being probable; likelihood.
2. n. A probable situation, condition, or event: Her election is a clear probability.
3. n. The likelihood that a given event will occur: little probability of rain tonight.
4. n. Statistics A number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences.
5. idiom. in all probability Most probably; very likely.

Century Dictionary and Cyclopedia

1. n. The state or character of being probable; likelihood; appearance of truth; that state of a case or question of fact which results from superior evidence or preponderation of argument on one side, inclining the mind to receive that as the truth, but leaving some room for doubt.
2. n. Quantitatively, that character of an argument or proposition of doubtful truth which consists in the frequency with which like propositions or arguments are found true in the course of experience. Thus, if a die be thrown, the probability that it will turn up ace is the frequency with which an ace would be turned up in an indefinitely long succession of throws. It is conceivable that there should be no definite probability: thus, the proportion of aces might so fiuctuate that their frequency in the long run would be represented by a diverging series. Yet even so, there would be approximate probabilities for short periods of time. All the essential features of probability are exhibited in the case of putting into a bag some black beans and some white ones, then shaking them well, and finally drawing out one or several at random. The beans must first be shaken up, so as to assimilate or generalize the contents of the bag; and a similar result must be attained in any case in which probability is to have any real significance. Next, a sample of the beans must be drawn out at random — that is, so as not to be voluntarily subjected to any general conditions additional to those of the course of experience of which they form a part. Thus, out-of-the-way ones or uppermost ones must not be particularly chosen. This random choice may be effected by machinery, if desired. If, now, a great number of single beans are so taken out and replaced successively, the following phenomenon will be found approximately true, or, if not, a prolongation of the series of drawings will render it so: namely, that if the whole series be separated into parts of two fixed numbers of drawings, say into series of 100 and of 10,000 alternately, then the average proportion of white beans among the sets of 100 will be nearly the same as the average proportion among the sets of 10,000. This is the fundamental proposition of the theory of probabilities — we might say of logic — since the security of all real inference rests upon it. The greater the frequency with which a specific event occurs in the long run, the stronger is the expectation that it will occur in a particular case. Hence, probability has been defined as the degree of belief which ought to be accorded to a problematical judgment; but this conceptualistic probability, as it is termed, is strictly not probability, but a sense of probability. Probability may be measured in different ways. The conceptualistic measure is the degree of confidence to which a reason is entitled; it is used in the mental process of balancing reasons pro and con. The conceptualistic measure is the logarithm of another measure called the odds — that is, the ratio of the number of favorable to the number of unfavorable cases. But the measure which is most easily guarded against the fallacies which beset the calculation of probabilities is the ratio of the number of favorable cases to the whole number of equally possible cases, or the ratio of the number of occurrences of the event to the total number of occasions in the course of experience. This ratio is called the probability or chance of the event. Thus, the probability that a die will turn up ace is ⅙. Probability zero represents impossibility; probability unity, certainty. The fundamental rules for the calculation of probabilities are two, as follows: Rule I. The probability that one or the other of two mutually exclusive propositions is true is the sum of the probabilities that one and the other are true. Thus, if ⅙ is the probability that a die will turn up ace, and ½ is the probability that it will turn up an even number, then, since it cannot turn up at once an ace and an even number, the probability that one or other will be turned up is ⅙ + ½ = ⅔. It follows that if p is the probability that any event will happen, 1 — p is the probability that it will not happen. Rule II. The probability of an event multiplied by the probability, if that event happens, that another will happen, gives as product the probability that both will happen. Thus, it a die is so thrown that the probability of its not being found is ½, then the probability of its being found ace up is ⅓ × ⅙ = . If the probability that a certain man will reach the age of forty is p, and the probability, when he is forty, that he will then reach sixty is q, then the probability now that he will reach sixty is pq. If two events A and B are such that the probability of A is the same whether B does or does not happen, then, also, the probability of B is the same whether A does or does not happen, and the events are said to be independent. The probability of the concurrence of two independent events is the product of their separate probabilities. The probability that a general event, whose probability on each one of n occasions is p, should occur just k times among these n occasions, is equal to the term containing p in the development of (p + q)^k, where q = 1 — p. Thus, suppose the event is the appearance of head when a coin is tossed up, so that p = q = ½, and the coin be tossed up six times. Then the probabilities of 0, 1, 2, 3, 4, 5, 6 heads respectively are , , , , , . . The most probable value of k is that whole number next less than (n + 1) p, unless this be itself a whole number, when it is equally probable. When the number of trials is large, the probabilities of the different numbers of occurrences of the given event are proportional to areas included between the so-called probability curve, its asymptote, and ordinates at successive distances equal to This probability curve, whose equation is y = 0 — 1σ—x (where o is the circumference for unit diameter, and σ is the Napierian base), is represented in the figure, where the approximate straightness of the slope will be remarked. If it is desired to ascertain the probability of the occurrence from k, to k₂ times inclusive in n trials of an event whose probable occurrence at each trial is p, the approximate value is the area included between the probability curve, the asymptote, and the two ordinates, for which Twice the quadratures of the areas are given in treatises on probabilities as tables of the theta function of probabilities. The chief practical application of probability is to insurance; and its only significance lies in an assurance as to the average result in the long run. The theory of probability is to be regarded as the logic of the physical sciences.
3. n. Anything that has the appearance of reality or truth.
4. n. A statement of what is likely to happen; a forecast: applied in the plural by Cleveland Abbe to his daily weather-predictions in Cincinnati in 1869, and subsequently adopted by General Myer to designate the official weather-forecasts of the United States Signal Service. The same term had been similarly used by Leverrier in Paris since 1859.

Wiktionary

1. n. the state of being probable; likelihood
2. n. an event that is likely to occur
3. n. the relative likelihood of an event happening
4. n. mathematics a number, between 0 and 1, expressing the precise likelihood of an event happening

GNU Webster's 1913

1. n. The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood.
2. n. That which is or appears probable; anything that has the appearance of reality or truth.
3. n. (Math.) Likelihood of the occurrence of any event in the doctrine of chances, or the ratio of the number of favorable chances to the whole number of chances, favorable and unfavorable. See 1st Chance, n., 5.

WordNet 3.0

1. n. a measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible
2. n. the quality of being probable; a probable event or the most probable event