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Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com
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What Are the Chances? Probability Probability Rules More About Chance ] Probability Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability > What Are the Chances? What Are the Chances? • Fundamentals of Probability • Conditional Probability • Unions and Intersections • Complementary Events Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/probability-8/what-are-the-chances-33/
Probability > Probability Rules Probability Rules • The Addition Rule • The Multiplication Rule • Independence • Counting Rules and Techniques • Bayes' Rule • The Collins Case Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/probability-8/probability-rules-34/
Probability > More About Chance More About Chance • The Paradox of the Chevalier De Méré • Are Real Dice Fair? Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/probability-8/more-about-chance-35/
Appendix Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability Key terms • Bayes' factorThe ratio of the conditional probabilities of the event given that is the case or that is the case, respectively. • combinatoricsA branch of mathematics that studies (usually finite) collections of objects that satisfy specified criteria. • conditional probabilityThe probability that an event will take place given the restrictive assumption that another event has taken place, or that a combination of other events has taken place • disjointHaving no members in common; having an intersection equal to the empty set. • equiprobablehaving an equal chance of occurring mathematically • eventA subset of the sample space. • exhaustiveincluding every possible element • experimentSomething that is done that produces measurable results, called outcomes. • independenceThe occurrence of one event does not affect the probability of the occurrence of another. • independentNot dependent; not contingent or depending on something else; free. • independentNot contingent or dependent on something else. • independent eventthe fact that occurs does not affect the probability that occurs Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability • multiplication ruleThe probability that A and B occur is equal to the probability that A occurs times the probability that B occurs, given that we know A has already occurred. • mutually exclusivedescribing multiple events or states of being such that the occurrence of any one implies the non-occurrence of all the others • outcomeOne of the individual results that can occur in an experiment. • pipone of the spots or symbols on a playing card, domino, die, etc. • Platonic solidany one of the following five polyhedra: the regular tetrahedron, the cube, the regular octahedron, the regular dodecahedron and the regular icosahedron • polynomialAn expression consisting of a sum of a finite number of terms: each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power. • probabilityThe relative likelihood of an event happening. • probability theoryThe mathematical study of probability (the likelihood of occurrence of random events in order to predict the behavior of defined systems). • prosecutor's fallacyA fallacy of statistical reasoning when used as an argument in legal proceedings. • random numbernumber allotted randomly using suitable generator (electronic machine or as simple "generator" as die) • sample spaceThe set of all possible outcomes of a game, experiment or other situation. • sample spaceThe set of all outcomes of an experiment. Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability • veridical paradoxa situation in which a result appears absurd but is demonstrated to be true nevertheless Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability Platonic Solids as Dice A Platonic solids set of five dice; tetrahedron (four faces), cube/hexahedron (six faces), octahedron (eight faces), dodecahedron (twelve faces), and icosahedron (twenty faces). Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."BluePlatonicDice."CC BY-SAhttp://en.wikipedia.org/wiki/File:BluePlatonicDice.jpgView on Boundless.com
Probability Coin Flip Often in sports games, such as tennis, a coin flip is used to determine who will serve first because heads and tails are complementary events. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Heads or tails."CC BY-SAhttp://commons.wikimedia.org/wiki/File:Heads_or_tails.jpgView on Boundless.com
Probability Bayes' Theorem A blue neon sign at the Autonomy Corporation in Cambridge, showing the simple statement of Bayes' theorem. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Bayes' Theorem MMB 01."CC BY-SAhttp://commons.wikimedia.org/wiki/File:Bayes'_Theorem_MMB_01.jpgView on Boundless.com
Probability The Collins Case The Collins case is a classic example of the prosecutor's fallacy. The guilty verdict was reversed upon appeal to the Supreme Court of California in 1968. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."CA SC seal."Public domainhttp://commons.wikimedia.org/wiki/File:CA_SC_seal.pngView on Boundless.com
Probability de Méré's Paradox de Méréobserved that getting at least one 6 with 4 throws of a die was more probable than getting double 6's with 24 throws of a pair of dice. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."6sided dice."CC BY-SAhttp://en.wikipedia.org/wiki/File:6sided_dice.jpgView on Boundless.com
Probability Die Dice are often used when learning the rules of probability. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Nuvola apps atlantik."CC BY-SAhttp://en.wikipedia.org/wiki/File:Nuvola_apps_atlantik.pngView on Boundless.com
Probability Union of Two Sets The shaded Venn Diagram shows the union of set (the circle on left) with set (the circle on the right). It can be written shorthand as . Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Venn0111."CC BY-SAhttp://en.wikipedia.org/wiki/File:Venn0111.svgView on Boundless.com
Probability Intersection of Two Sets Set is the circle on the left, set is the circle on the right, and the intersection of and , or , is the shaded portion in the middle. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Venn0001."CC BY-SAhttp://en.wikipedia.org/wiki/File:Venn0001.svgView on Boundless.com
Probability Independent Events Selecting two cards from a deck by first selecting one, then replacing it in the deck before selecting a second is an example of independent events. Free to share, print, make copies and changes. Get yours at www.boundless.com Flickr."All sizes | Ace of Spades Card Deck Trick Magic Macro 10-19-09 2 | Flickr - Photo Sharing!."CC BYhttp://www.flickr.com/photos/stevendepolo/4028160820/sizes/o/in/photostream/View on Boundless.com
Probability Attribution • Wikipedia."Probability axioms."CC BY-SA 3.0http://en.wikipedia.org/wiki/Probability_axioms • Wiktionary."sample space."CC BY-SA 3.0http://en.wiktionary.org/wiki/sample_space • Wiktionary."disjoint."CC BY-SA 3.0http://en.wiktionary.org/wiki/disjoint • Wiktionary."independent."CC BY-SA 3.0http://en.wiktionary.org/wiki/independent • Wikipedia."Bayes' theorem."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bayes'_theorem • Wikipedia."Conditional probability."CC BY-SA 3.0http://en.wikipedia.org/wiki/Conditional_probability • Wiktionary."conditional probability."CC BY-SA 3.0http://en.wiktionary.org/wiki/conditional_probability • Wiktionary."independent."CC BY-SA 3.0http://en.wiktionary.org/wiki/independent • Wikipedia."Union (set theory)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Union_(set_theory) • Wiktionary."disjoint."CC BY-SA 3.0http://en.wiktionary.org/wiki/disjoint • Wikipedia."Intersection (set theory)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Intersection_(set_theory) • Wiktionary."independent."CC BY-SA 3.0http://en.wiktionary.org/wiki/independent • Wikipedia."Complementary event."CC BY-SA 3.0http://en.wikipedia.org/wiki/Complementary_event • Wiktionary."mutually exclusive."CC BY-SA 3.0http://en.wiktionary.org/wiki/mutually_exclusive • Wiktionary."exhaustive."CC BY-SA 3.0http://en.wiktionary.org/wiki/exhaustive • Wikipedia."Probability axioms."CC BY-SA 3.0http://en.wikipedia.org/wiki/Probability_axioms • Wikipedia."addition rule."CC BY-SA 3.0http://en.wikipedia.org/wiki/addition%20rule Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability • Wiktionary."probability."CC BY-SA 3.0http://en.wiktionary.org/wiki/probability • Wikipedia."Probability."CC BY-SA 3.0https://en.wikipedia.org/wiki/Probability • Wikidot."Some rules of probability - Statistics."CC BY-SAhttp://statistics.wikidot.com/ch5 • Wiktionary."sample space."CC BY-SA 3.0http://en.wiktionary.org/wiki/sample_space • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/multiplication-rule • Wikidot."Some rules of probability - Statistics."CC BY-SAhttp://statistics.wikidot.com/ch5 • Wikipedia."Independence (probability theory)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Independence_(probability_theory) • Wikipedia."independence."CC BY-SA 3.0http://en.wikipedia.org/wiki/independence • Wiktionary."probability theory."CC BY-SA 3.0http://en.wiktionary.org/wiki/probability_theory • OpenStax CNX."Roberta Bloom, Probability Topics: Independent & Mutually Exclusive Events (modified R. Bloom). September 17, 2013."CC BY 3.0http://cnx.org/content/m18868/latest/ • Wikipedia."Combinatorics."CC BY-SA 3.0http://en.wikipedia.org/wiki/Combinatorics • Wikipedi."Pigeonhole principle."CC BY-SA 3.0https://en.wikipedia.org/wiki/Pigeonhole_principle • Wikipedia."Bijective proof."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bijective_proof • Wikipedia."Double counting (proof technique)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Double_counting_(proof_technique) • Wikipedia."Bijection."CC BY-SA 3.0https://en.wikipedia.org/wiki/Bijection • Wikipedia."Inclusion-exclusion principle."CC BY-SA 3.0https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle • Wiktionary."polynomial."CC BY-SA 3.0http://en.wiktionary.org/wiki/polynomial • Wiktionary."combinatorics."CC BY-SA 3.0http://en.wiktionary.org/wiki/combinatorics • Wikipedia."Combinatorial principles."CC BY-SA 3.0http://en.wikipedia.org/wiki/Combinatorial_principles Free to share, print, make copies and changes. Get yours at www.boundless.com
Probability • Wikipedia."Bayes' rule."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bayes'_rule • Wikipedia."Bayesian inference."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bayesian_inference • Wikipedia."Bayes' theorem."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bayes'_theorem • Wikipedia."Bayes' factor."CC BY-SA 3.0http://en.wikipedia.org/wiki/Bayes'%20factor • Wikipedia."Prosecutor's fallacy."CC BY-SA 3.0http://en.wikipedia.org/wiki/Prosecutor's_fallacy • Wikipedia."People v. Collins."CC BY-SA 3.0http://en.wikipedia.org/wiki/People_v._Collins • Wikipedia."prosecutor's fallacy."CC BY-SA 3.0http://en.wikipedia.org/wiki/prosecutor's%20fallacy • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/multiplication-rule • Wikipedia."Antoine Gombaud."CC BY-SA 3.0http://en.wikipedia.org/wiki/Antoine_Gombaud • Wiktionary."equiprobable."CC BY-SA 3.0http://en.wiktionary.org/wiki/equiprobable • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/independent-event • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/veridical-paradox • Proof Wiki.GNU FDLhttp://www.proofwiki.org/wiki/De_M%C3%A9r%C3%A9's_Paradox • Wikipedia."Dice."CC BY-SA 3.0http://en.wikipedia.org/wiki/Dice • Wiktionary."pip."CC BY-SA 3.0http://en.wiktionary.org/wiki/pip • Wiktionary."random number."CC BY-SA 3.0http://en.wiktionary.org/wiki/random_number • Wiktionary."Platonic solid."CC BY-SA 3.0http://en.wiktionary.org/wiki/Platonic_solid Free to share, print, make copies and changes. Get yours at www.boundless.com