# probability

## Definitions

• Although most Jamestown workshops were probably made of framework and were merely sheds, one brick foundation has three brick fireboxes and a large brick chimney. This structure was probably a brew house, bakery, or distillery
• WordNet 3.6
• n probability the quality of being probable; a probable event or the most probable event "for a while mutiny seemed a probability","going by past experience there was a high probability that the visitors were lost"
• n probability 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 "the probability that an unbiased coin will fall with the head up is 0.5"
• *** Near the foundation of the probable bake shop, a pair of kilns once served for slaking lime, and perhaps for firing...

Webster's Revised Unabridged Dictionary
• Interesting fact: Thomas Watson, who was the chairman of IBM in 1943 predicted that their would probably only be a world market for five computers.
• Probability (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.
• Probability That which is or appears probable; anything that has the appearance of reality or truth. "The whole life of man is a perpetual comparison of evidence and balancing of probabilities .""We do not call for evidence till antecedent probabilities fail."
• Probability The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood. "Probability is the appearance of the agreement or disagreement of two ideas, by the intervention of proofs whose connection is not constant, but appears for the most part to be so."
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Century Dictionary and Cyclopedia
• Interesting fact: The largest item on any menu in the world is probably the roast camel, sometimes served at Bedouin wedding feasts. The camel is stuffed with a sheep's carcass, which is stuffed with chickens, which are stuffed with fish, which are stuffed with eggs.
• n probability 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.
• n probability 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. 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.
• n probability Anything that has the appearance of reality or truth.
• n probability 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.
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Chambers's Twentieth Century Dictionary
• Interesting fact: The oldest musical instrument is probably the flute. It's been discovered that primitive cave dwellers made an instrument from bamboo or some other small hollow wood.
• Probability quality of being probable: appearance of truth: that which is probable: chance or likelihood of something happening:—pl. Probabil′ities
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## Quotations

• Jones “Anyone who profits from the experience of others probably writes biographies.”
• Franz Kafka “My fear... is my substance, and probably the best part of me.”
• Peter Laurence “If you're not sure where you're going, you'll probably end up somewhere else.”
• Elbert Hubbard “The man who does not understand your silence will probably not understand your words.”
• Clive James “Anyone afraid of what he thinks television does to the world is probably just afraid of the world.”
• James H. Robinson “We find it hard to believe that other people's thoughts are as silly as our own, but they probably are.”

## Etymology

Webster's Revised Unabridged Dictionary
L. probabilitas,: cf. F. probabilité,
Chambers's Twentieth Century Dictionary
Fr.,—L. probabilisprobāre, -ātum, to prove.

## Usage

### In literature:

Probably waiting for Jason to begin playing seriously.
"Deathworld" by Harry Harrison
It probably would thrive best in the shade, as it is found in copses.
"The plant-lore and garden-craft of Shakespeare" by Henry Nicholson Ellacombe
And now I must sell all, probably to the same merchant and probably at a loss.
"The Saracen: The Holy War" by Robert Shea
Probably he was a reserve officer.
"The Electronic Mind Reader" by John Blaine
It's very probable that you will see her in the next half-hour.
"The Greater Power" by Harold Bindloss
He will probably live to be the Marquis of Brotherton.
"Is He Popenjoy?" by Anthony Trollope
He knows that he will probably have to work harder than he would ever have worked on the farm.
"The Shepherd of the North" by Richard Aumerle Maher
Knowing the two, as I do, I feel the probability to be on their side.
"Marion Fay" by Anthony Trollope
The cause is not known, but the disease is probably due to chilling.
"Special Report on Diseases of Cattle" by U.S. Department of Agriculture
But this is probably valueless.
"When Ghost Meets Ghost" by William Frend De Morgan
What the terms were, or were to be, it is probable we never shall know; or what is more probable, that feigned ones, if any, will be given.
"The Writings Of Thomas Paine, Complete" by Thomas Paine
Nothing, indeed, is more probable; it is when we have the facts and trace out cause and effect that we are in a fair way to do good.
"Psychology" by Robert S. Woodworth
Still it could be endured and there was happiness and peace in store for him probably.
"The "Genius"" by Theodore Dreiser
The conclusion was that probably nothing could be done.
"The Flaming Mountain" by Harold Leland Goodwin
The answer probably is easy as pie once we find the key.
"The Caves of Fear" by John Blaine
It was possible, but not probable.
"The Golden Skull" by John Blaine
He was born at Venice, probably about 1560, and is said to have been of Flemish descent.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 2" by Various
We probably concluded that he could do no good.
"Forty Years in the Wilderness of Pills and Powders" by William A. Alcott
Between these ranges, which are probably permanently snowy to about 27 deg.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7" by Various
Probably better than you do.
"Caribbee" by Thomas Hoover
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### In poetry:

You'll probably find
to be a bit cleverer
than you look.
"Meeting the Eye" by Piet Hein
Now I wait your probable death,
I, who was a fact of earth,
Never held a fainting faith
In Buddha or in Christ’s belief.
"Mother" by Dorothy Violet Wellesley
Faith uses means, but rests on none;
Sense sails when outward means are gone:
Trusts more on probabilities,
Than all the divine promises.
"The Believer's Principles : Chap. IV." by Ralph Erskine
"But, being a man of doubtless worth,
If you feel certain quite
That we were probably changed at birth,
I'll venture to say you're right."
"General John" by William Schwenck Gilbert
Now should I find th' ill-natur'd Muse
Her kind assistance shall refuse;
And 'tis most probable she will,
As follows, I would guide the quill.
"The Wager" by William Hutton
The Hidden Law does not deny
Our laws of probability,
But takes the atom and the star
And human beings as they are,
And answers nothing when we lie.
"The Hidden Law" by W H Auden

### In news:

Roger Clemens's Long, Expensive, and Probably Useless Trial.
The last time you bit into a ripe, juicy tomato or strawberry you probably didn't give it a second thought.
It was probably hot out and perhaps you stopped for gas, food or just to stretch your legs.
Scott Seabol is an 88th-round draft pick who played in Class A this year and probably will never make it into pinstripes at Yankee Stadium.
I probably shouldn't share this with you, but I have been arguing with my wife.
It's probably a safe bet that you or someone you know went to see The Dismemberment Plan this weekend.
I couldn't see all those faces, but I knew they were there: quiet, probably wide-eyed.
This yearling bear was probably kicked out recently by his or her mommy bear.
Mike Helfgot on boys basketball blog Simeon probably will have to beat Simeon.
If you're like me, you're probably prone to skimp on shut-eye as the holiday craziness starts to go into full effect.
If you've been to a movie comedy in the last few years, you probably know Seth Rogen.
Before he was even asked a question about his first pick as coach of the Tampa Bay Buccaneers , Greg Schiano was painting a portrait that probably still is invisible to most Tampa Bay fans.
A Sterling man jogging on the Rail Trail in Holden was slightly injured by buckshot, probably from a hunting gun, on Wednesday, Dec 1.
Well, it's probably no surprise that you are not alone.
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### In science:

In section II we recall the connection between the survival probability ΦN (t) and the so-called ﬁxed trap survival probability (i.e., the survival probability when the trap is placed at a given distance) and give the basics of the extended Rosenstock approximation.
Multiparticle trapping problem in the half-line
It is worth emphasizing that if these probabilities were independent of each other, the probability to ﬁnd a completely order band would be the product of the probabilities for each state, i.e., the product of the diagonal elements of the matrices shown in Tables II, III and IV.
A study of randomness, correlations and collectivity in the nuclear shell model
In each step the RW will vary his direction with probability p: at right with probability p/2 or at left with the same probability.
Small-Worlds, Mazes and Random Walks
More precisely we introduce the quantity sT (i, c) that is deﬁned as the probability of ﬁnding pT (i, c) = 1, in the same way sF (i, c) is the probability of ﬁnding pT (i, c) = 0 and sI (i, c) is the probability of ﬁnding 0 < pT (i, c) < 1.
On the probabilistic approach to the random satisfiability problem
The transition probabilities of RWIDF are p(cid:0)(g , x), (gh, y )(cid:1) = p(x, y )µx,y (h) (assuming that X is countable), where µx,y are probability measures on X , and p(x, y ) are the transition probabilities of the quotient chain on X .
Boundaries and harmonic functions for random walks with random transition probabilities
In the sequel, we will consider the two following probability spaces: • the set An of words with length n, endowed with the uniform probability Pn , • the set Ln of Lyndon words with length n, endowed with the uniform probability ˜Pn .
Limit law of the standard right factor of a random Lyndon word
Large random matrices and free probability Free probability is a probability theory in a non-commutative framework.
Large deviations and stochastic calculus for large random matrices
Free probability is not only a theory of probability for non-commutative variables; it contains also the central notion of freeness, which is the analogue of independence in standard probability.
Large deviations and stochastic calculus for large random matrices
In Eq. (15), p+ , p− , and p0 are the probabilities of occurrence for the three types of cavity ﬁeld surveys. P+ (k) is a probability distribution over positive integers k ; and P− (k) is a probability distribution over negative integers k .
Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random \$K\$-satisfiability problem
Under the assumption on the probability space we can deﬁne a pair of random variables (X, Y ) to be (x, y) with probability θ and (x′ , y ′ ) with probability (1 − θ).
Moment inequalities for functions of independent random variables
Hence, the probability that Gn has a bad component is bounded by o(1) (the probability that C1 is too small) plus the probability that some component C 6= C1 of G′′ n containing at least A log n/k vertices of S1 sends no edges to C1 in Gn .
The phase transition in inhomogeneous random graphs
Under optimal play, the probability that Short wins is just the probability that there is a path from the root to some leaf when each edge is independently deleted with probability 1/2.
Random-Turn Hex and other selection games
RG are probably due to the strong restriction, deﬁned as the connection probability equals the repair probability, prg = pre .
Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy
By a Gaussian probability distribution G , we mean the one-dimensional real Gaussian probability distribution with mean 0 and variance 1, i. e., for x ∈ R, the probability density of G at x is e−x2 /2 .
Random measurement bases, quantum state distinction and applications to the hidden subgroup problem
Say that the prior probability of a subset only depends on the size of the subset and that the probability of a given size k , is proportional to the probability that a Geometric (1 − α) random variable takes the value k .
Nonparametric Bayesian Classification
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