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Probability Quotes

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Probability Quotes

“We either base our 'confidence' on reason (evident probabilities, past experience, competence, etc) or we base our beliefs on faith, which is blind by definition. Faith is the most dishonest position it is possible to have, because it is an assertion of stoic conviction that is assumed without reason and defended against all reason. If you have to believe it on faith, you have no reason to believe it at all.”

“He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.”

“A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.”

“Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.”

“We’re just two out of billions of people, on a rock orbiting a ball of fire, alive at a point in time that allows us to witness humanity make the biggest, most bewildering discoveries. Two people who could have been anywhere in the world, separated by time, space, circumstances. Yet after all we’ve been through, all that’s happened to us, here we are, now. Sharing this moment together. We’re not insignificant. We’re miracles.”

“Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the die will come up proximately 1 ,000,000,000 times) and the improbable (that in six throws with the same die the one will come approximately up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable. But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term "probability" includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification. Cf. Ernst Mally's Probability and Law, Hans Reichenbach The theory Probability, Whitehead and Russell's Principia Mathematica, von Mises' Probability, Statistics and Truth”

“The Coin of Life example: Say you have a coin with heads on one side and tails on the other side. One side would mean good and the other bad, based on your interpretation or bet of which side of the coin represents a win for you. However, you can't decide the outcome and the coin flips many times throughout your life. Finding balance is flipping the coin in such a way that neither of the sides is of greater importance to you, but if the coin lands on the middle bit, you realize that the space between what you consider good or bad is so small and the probability of landing there is also incredibly small without continuous practice. However, no matter the outcome, you choose to accept the coin as it is, with both sides, and appreciate the importance of both in your life. For the coin of life has meaning and value no matter what side it lands on. It's each individual's choice whether to bet on the outcome or not, but ultimately your coin of life will be spent somehow.”

“One of the recent arguments from design, that based on the so-called fine-tuning life of some fundamental physical constants, founders on the following objections: an extremely small prior probability merited by the God of theism in light – if that is the right word – of the Problem of Evil; the fact that it is not unreasonable to place a substantial probability on the hypothesis that a future theory will fix those values; and the sheer incoherence of computations of the ‘chances’ of fine-tuning were there no fine-tuner.”

“There is always opportunity cost in choosing one path over others. The betting elements of decisions—choice, probability, risk, etc.—are more obvious in some situations than others. Investments are clearly bets. A decision about a stock (buy, don’t buy, sell, hold, not to mention esoteric investment options) involves a choice about the best use of financial resources. Incomplete information and factors outside of our control make all our investment choices uncertain. We evaluate what we can, figure out what we think will maximize our investment money, and execute. Deciding not to invest or not to sell a stock, likewise, is a bet. These are the same decisions I make during a hand of poker: fold, check, call, bet, or raise.”

“The wave quality of light is the same as that of the electron. The wave determines the probable location of the photon of light when it is detected. The wave character of light is not vibrating stuff like a wave of water but rather a wavelike function encoding information about where you'll find the photon of light once it is detected. Until it reaches the detector plate, like the electron, it is seemingly passing through both slits simultaneously, making its mind up about its location only once it is observed [...]. It's this act of observation that is such a strange feature of quantum physics. Until I ask the detector to pick up where the electron is, the particle should be thought of as probabilistically distributed over space, with a probability described by a mathematical function that has wavelike characteristics. The effect of the two slits on this mathematical wave function alters it in such a way that the electron is forbidden from being located at some points on the detector plate. But when the particle is observed, the die is cast, probabilities disappear, and the particle must decide on a location.”

“A more serious consequence of the illusion of control is revealed in our preference for driving over flying. At least part of this irrational—from a survival point of view—habit is due to the fact that we “feel in control” when driving, but not when flying. The probability of dying in a cross-country flight is approximately equal to the probability of dying in a 12-mile drive— in many cases, the most dangerous part of the trip is over when you reach the airport (Sivak & Flannagan, 2003). Gerd Gigerenzer (2006) estimates that the post-9/11 shift from flying to driving in the United States resulted in an additional 1,500 deaths, beyond the original 3,000 immediate victims of the terrorist attacks.”

“Another situation in which we attend to base rates occurs if people ascribe some causal significance to discrepant rates. When they can see the causal relevance of the base rates, they often incorporate them into their reasoning. For example, the belief that one bus company has more accidents than another because its drivers are more poorly selected and trained will influence mock jurors to take this difference in accident rates into account in evaluating eyewitness testimony; but belief that a bus company has more accidents simply because it is larger will not. Study after study has shown that when these rates are merely statistical as opposed to causal, they tend to be ignored. Exactly the same effect seems to occur in real courtrooms; naked statistical evidence is notoriously unpersuasive.”

“Keep trying; failures increase the probability of success.”

“Conventional wisdom nor scientific, mathematical prove of randomness in life could do nothing to deter human's curiosity for the unknown, however small the chance of a positive outcome maybe.”

“Time did exist here, in small amounts (well some of the time) – and there were feint eddies and currents of time here, things that were barely tangible. Feint forces of the universe they were, nearly indiscernible from the nothingness like a warm breeze on a hot summer night. How long he had been here, he knew not – but he was slowly learning to master these barely tangible waves like a new surfer with one foot on the sandy beach and the other on a shiny new board of Hatred. Revenge splashed around his feet like the cold waves of the ocean of Time. Nearby, two other inmates collided with each other, bounced apart spread-eagled and spiraled off into the distance in infinite slowness. The Wetsuit of Insanity clung to his spiritual body, isolating him from the timelessness that seemed to exist here. A wind of Change blew at him from behind and he pushed off from the beach with iron determination and a mental clarity hereto before unknown to him. Something in the microcosm that didn’t even have a name went ‘bling’ and against all the laws of probability, Brad Xyl opened his eyes.”

“4. Religion. Your reason is now mature enough to examine this object. In the first place, divest yourself of all bias in favor of novelty & singularity of opinion... shake off all the fears & servile prejudices, under which weak minds are servilely crouched. Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason, than that of blindfolded fear. You will naturally examine first, the religion of your own country. Read the Bible, then as you would read Livy or Tacitus. The facts which are within the ordinary course of nature, you will believe on the authority of the writer, as you do those of the same kind in Livy and Tacitus. The testimony of the writer weighs in their favor, in one scale, and their not being against the laws of nature, does not weigh against them. But those facts in the Bible which contradict the laws of nature, must be examined with more care, and under a variety of faces. Here you must recur to the pretensions of the writer to inspiration from God. Examine upon what evidence his pretensions are founded, and whether that evidence is so strong, as that its falsehood would be more improbable than a change in the laws of nature, in the case he relates. For example in the book of Joshua we are told the sun stood still several hours. Were we to read that fact in Livy or Tacitus we should class it with their showers of blood, speaking of statues, beasts, &c. But it is said that the writer of that book was inspired. Examine therefore candidly what evidence there is of his having been inspired. The pretension is entitled to your inquiry, because millions believe it. On the other hand you are astronomer enough to know how contrary it is to the law of nature that a body revolving on its axis as the earth does, should have stopped, should not by that sudden stoppage have prostrated animals, trees, buildings, and should after a certain time have resumed its revolution, & that without a second general prostration. Is this arrest of the earth's motion, or the evidence which affirms it, most within the law of probabilities? You will next read the New Testament. It is the history of a personage called Jesus. Keep in your eye the opposite pretensions: 1, of those who say he was begotten by God, born of a virgin, suspended & reversed the laws of nature at will, & ascended bodily into heaven; and 2, of those who say he was a man of illegitimate birth, of a benevolent heart, enthusiastic mind, who set out without pretensions to divinity, ended in believing them, and was punished capitally for sedition, by being gibbeted, according to the Roman law, which punished the first commission of that offence by whipping, & the second by exile, or death in fureâ. ...Do not be frightened from this inquiry by any fear of its consequences. If it ends in a belief that there is no God, you will find incitements to virtue in the comfort and pleasantness you feel in its exercise, and the love of others which it will procure you... In fine, I repeat, you must lay aside all prejudice on both sides, and neither believe nor reject anything, because any other persons, or description of persons, have rejected or believed it... I forgot to observe, when speaking of the New Testament, that you should read all the histories of Christ, as well of those whom a council of ecclesiastics have decided for us, to be Pseudo-evangelists, as those they named Evangelists. Because these Pseudo-evangelists pretended to inspiration, as much as the others, and you are to judge their pretensions by your own reason, and not by the reason of those ecclesiastics. Most of these are lost... [Letter to his nephew, Peter Carr, advising him in matters of religion, 1787]”

“Perhaps the fundamental precept of probabilistic analysis is the exhortation to take a bird’s-eye, distributional view of the situation under analysis (e.g., a dice game, the traffic in Boulder, crimes in Pittsburgh, the situation with that troublesome knee) and to define a sample space of all the possible events and their logical, set membership interrelations. This step is exactly where rational analysis and judgments based on availability, similarity, and scenario construction diverge: When we judge intuitively, the mind is drawn to a limited, systematically skewed subset of the possible events. In the case of scenario construction, for example, we are often caught in our detailed scenario—focused on just one preposterously specific outcome path.”

“You have a very high probability of your quote and your name being distributed, posted, and shared around the world!”

“Keynes concluded that citizens both rich and poor would have to be led gradually out of capitalism, a base and repugnant system of morals. His fellow liberals in the 1920s debated the morality and efficacy of capitalism, as well as the correctness of the view that, as one Liberal politician put it, “man’s primary concern is to satisfy in ever ampler degree his physical needs.” For Keynes, this might be human nature, but his entanglement with Bateson and Pearson had immersed him in the notion that biological nature was malleable. Greed would be driven out not just by education but by the eugenic cultivation of “special talents.” It would be replaced by “some of the most sure and certain principles of religion and traditional virtue—that avarice is a vice, that the exaction of usury is a misdemeanour, and the love of money is detestable, that those walk most truly in the paths of virtue and sane wisdom who take least thought for the morrow.” In the meantime, however, Keynes conceded capitalism’s efficacy. In order to improve productivity to the point where everyone’s needs could be easily satisfied, the coming century still demanded devotion to the god of greed. The goal of the next hundred years of capitalism would be its own extirpation.”