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“The most important questions of life are indeed, for the most part, really only problems of probability.” Pierre Simon Laplace Théorie Analytique des Probabilités, 1812

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“ The theory of probability as a mathematical discipline can and should be developed from axioms in exactly the same way as geometry and algebra.” Andrei Kolmogorov Foundations of the Theory of Probability, 1933

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“I think you’re begging the question,’’ said Haydock, “and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that!” Agatha Christie The Mirror Crack’d

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“There is no problem in all mathematics that cannot be solved by direct counting.” Ernest Mach

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I’m very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical. About binomial theorem I’m teeming with a lot o’ news, With many cheerful facts about the square of the hypoteneuse. Gilbert and Sullivan, Pirates of Penzance

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“Suam habet fortuna rationem.” (Chance has its reasons.) Petronius (First century, A.D.)

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“The conception of chance enters into the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception than causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation.” Max Born, 1882-1970

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“Iacta alea est.” (The die is cast.) Julius Caesar, Upon crossing the Rubicon 49 B.C.E

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“How many really basic mathematical objects are there? One is surely the ‘miraculous jar’ of the positive integers 1, 2, 3,.. Another is the concept of a fair coin. Though gambling was rife in the ancient world and although prominent Greeks and Romans sacrificed to Tyche, the goddess of luck, her coin did not arrive on the mathematical scene until the Renaissance. Perhaps one of the things that had delayed this was a metaphysical position which held that God speaks to humans through the action of chance.... The modern theory begins with the expulsion of Tyche from the Pantheon. There emerges the vision of the fair coin, the biased coin. This coin exists in some mental universe and all modern writers on probability theory have access to it. They toss it regularly and they speculate about what they ‘observe.’” Philip Davis and Reuben Hersh, The Mathematical Experience

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“It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.” Pierre Simon Laplace Théorie Analytique des Probabilités, 1812

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“The odds? A dissertation may be needed in the mathematical journals, but it seems the odds may be 1 in 10 million (from a U. of Rochester math professor), to 1 in 1,890 trillion (according to a Harvard math professor), to 1 in 8.7 million (according to the National Hole-in-One Foundation of Dallas), to 1 in 332,000 according to Golf Digest Calculator, who added that, statistically, this will not happen again in 190 years.” Boston Globe, 1989, reporting on the U.S. Open when 4 golfers, all using 7 irons, scored holes-in-one on the 6 th hole of the course, in less than two hours

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“Coincidences, in general, are great stumbling blocks in the way of that class of thinkers who have been educated to know nothing of the theory of probabilities---that theory to which the most glorious objects of human research are indebted for the most glorious of illustrations.” Edgar Allen Poe The Murders in the Rue Morgue

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“A striking example was the number of soldiers killed by horse kicks per year per Prussian army corps. Fourteen corps were examined, each for 20 years. For over half the corps-year combinations there were no deaths from horse kicks; for the other combinations the number of deaths ranged up to four. Presumably the risk of lethal horse kicks varied over years and corps, yet the overall distribution was remarkably well fitted by a Poisson distribution.” International Encyclopedia of the Social Sciences entry for Ladislaus Josephowitsch Bortkiewicz, The Law of Small Numbers, 1898

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“Misunderstanding of probability may be the greatest of all impediments to scientific literacy.” Stephen Jay Gould

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“There are two times in a man’s life when he should not speculate; when he can’t afford it, and when he can.” Mark Twain

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Hugh: I'll get the dictionary. Lisa: Why? Hugh: You'll see when you get there: the word ‘stochastic’. Lisa: “Pertaining to a process involving a randomly-determined sequence of observations.” (Laughs. They look at each other, then embrace passionately.) The Simpsons Lisa's Wedding

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“The ‘Law of Frequency Of Error’... reigns with serenity and in complete self- effacement amidst the wildest confusion. The huger the mob... the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand... an unsuspected and most beautiful form of regularity proves to have been latent all along.” Francis Galton

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“The world of science lives fairly comfortably with paradox. We know that light is a wave, and also that light is a particle. The discoveries made in the infinitely small world of particle physics indicate randomness and chance, and I do not find it any more difficult to live with the paradox of a universe of randomness and chance and a universe of pattern and purpose than I do with light as a wave and light as a particle. Living with contradiction is nothing new to the human being.” Madeline L'Engle (author of A Wrinkle in Time)

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“ Steinhaus, with his predilection for metaphors, used to quote a Polish proverb, ‘Forturny kolem sie tocza’ [Luck runs in circles], to explain why π, so intimately connected with circles, keeps cropping up in probability theory and statistics, the two disciplines which deal with randomness and luck.” Mark Kac, Enigmas of Chance

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“The record of a month’s roulette playing at Monte Carlo can afford us material for discussing the foundations of knowledge.” Karl Pearson

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“Probability does pervade the universe, and in this sense, the old chestnut about baseball imitating life really has validity. The statistics of streaks and slumps, properly understood, do teach an important lesson about epistemology, and life in general. The history of a species, or any natural phenomenon, that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he’s at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor!” Stephen Jay Gould

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“It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once.” Sir Francis Galton

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“Ideal Toy Company stated on the package of the original Rubik's cube that there were more than 3 billion possible states the cube could attain. This is analogous to McDonald's announcing that they've sold more than 120 hamburgers.” John Allen Paulos, Innumeracy

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“I dreamt that I was in Hell, and that Hell is a place full of all those happenings that are improbable but not impossible... There is a special department of Hell for students of probability. In this department there are many typewriters and many monkeys. Every time that a monkey walks on a typewriter, it types by chance one of Shakespeare’s sonnets.” Andre Bumblowski’s nightmare as related to Bertrand Russell

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“Therefore, this is the problem which I now set forth and make known after I have pondered over it for 20 years. Both its novelty and its very great usefulness, coupled with its just as great difficulty, can exceed in weight and value all the remaining chapters of this thesis.” Jacob D. Bernoulli, Ars Conjectandi (concerning the Law of Large Numbers)

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Dilbert writes a poem and presents it to Dogbert: Dogbert: I once read that given infinite time, a thousand monkeys with typewriters would eventually write the complete works of Shakespeare. Dilbert: But what about my poem? Dogbert: Three monkeys, ten minutes. Scott Adams, Dilbert comic stripe, May 15, 1989

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1-1 Copyright © 2015, 2010, 2007 Pearson Education, Inc. Chapter 13, Slide 1 Chapter 13 From Randomness to Probability.

1-1 Copyright © 2015, 2010, 2007 Pearson Education, Inc. Chapter 13, Slide 1 Chapter 13 From Randomness to Probability.

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