Slides Week 1 - WELCOME TO M118 While youre waiting PUZZLE...

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WELCOME TO M118! PUZZLE: 3 men walk into a hotel, expecting to pay $30 for a room. They each give the clerk $10, who, upon receiving the money, informs the men that there is a special today, rooms are only $25. He begins to return the $5 to the men, but, upon realizing that he cannot easily split the $5 three ways, he gives each man back $1 and gives the remaining $2 to the bellboy. So, each man ended up paying $9, plus the $2 given to the bellboy, for a total of $27 + $2 = $29. WHAT HAPPENED TO THE OTHER DOLLAR?????????? While you’re waiting…
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YOUR FIRST ASSIGNMENT! 1.) Log onto the M118 Oncourse Webpage via: http://www.iub.edu 2.) Download and read the Class Syllabus. 3.) Download and read the Departmental Course Outline. 4.) Download and save the Powerpoint slides for Week 1. (located on the M118 RESOURCES Page of Oncourse) 5.) Do the Welcome Set on the Webwork Homework System (located on the M118 TOOLS Page of Oncourse)
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PROBABILITY MODELS (the application of Set Theory to the study of random events)
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Part 1 – Review of Set Theory DEFN: A SET is a collection of “things”, called elements. TWO WAYS TO DESCRIBE SETS: Method 1: List the elements: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} or S = {1, 3, 4, 2, 5, 7, 10, 8, 6, 9} NOTE: 3 W S but 12 W S Method 2: Use a rule: read “the set of all things x such that x…” S = {x : x is a positive integer less than 11}
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S = { } = the empty set ( ) is the smallest set we will need to work with……
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Q: What is the LARGEST set we will need to work with?
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The largest set we will need to think about is….. DEFN: A Universal Set is the largest set that needs to be considered for a given “selection problem”.
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A selection problem: Suppose the members of AC/DC get tired of their name, so they decide to pick some new letters to be their new name. What is a reasonable Universal Set for this problem?
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U = {a, b, c, … , x, y, z} How’s about…………
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SIX WAYS to form new sets from other sets:
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1.) form a SUBSET of elements from a given set: DEFN: A set A is a subset of a set B if every element in A is also in B. A ( B is read “A is a subset of B”, and B ( A is ALSO read “A is a subset of B”
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Example: Let A = { a, b, c, d, e, f, g, h, i, j } B = { c, e, f }, and C = {b, c, e, f, k } Which of the following are true statements? a.) A B c.) A A b.) C B d.) B
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Example: Let A = { a, b, c, d, e, f, g, h, i, j } B = { c, e, f }, and C = {b, c, e, f, k } Which of the following are true statements? a.) A B (False) c.) A A (true for any A) b.) C B (True)d.) B (true for any B)
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2.) Form the UNION of two sets A B = the set of all of the elements * that are either in A or in B “union” or in both . KEYWORD “OR”
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EX: Let A = { a, b, c, x, y, z } & B = { d, e, f, x, y, z } Then A B = ??
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EX: Let A = { a, b, c, x, y, z } & B = { d, e, f, x, y, z } Then A ( B = { a, b, c, d, e, f, x, y, z } NOTE!! We never list elements in a set twice!!!
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