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Chapters 14 and 15-1 - Ch 14 From randomness to Probability...

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Unformatted text preview: Ch. 14 From randomness to Probability Some Terminology 1. Phenomenon consists of trials with an outcome 2. Relative frequency: # of outcomes in trial divided by the total number of outcomes possible Ch. 14/15 From randomness to Probability General Framework in Probability • Random Experiment , its Outcomes, Events and their Probabilities • At the outset, we consider an experiment , e.g. toss of a coin, roll of a die, or drawing a ball from an urn (say). • Associated with the given random experiment are its following principal characteristics: • Sample Space: • Events: • Probability: Function on the sample space and its events Chapters 14 and 15 : Probability Algebra of Events • Sample space : The collection of all possible outcomes in an experiment. • It contains every outcome and denoted by S. Chapters 14 and 15 : Probability • Event: It is a certain subset of outcomes from the sample space S, usually denoted by capital letters, A; B; … A Chapters 14 and 15 : Probability • Complement of an event A. It contains all outcomes not in A. • Notation: A c A c A c A c A Intersection of two events A and B contains all those outcomes that are common to both A and B. The Intersection event is also called the “and” event Notation: B A Union of two events A and B contains all those outcomes that are in at least one of the two given events, i.e. either in A or B or both. The union event is also called the “or” event Notation: B A ∪ Disjoint Events (mutually exclusive): A and B can not occur simultaneously. For such events the intersection event is empty and is called the null event. Class Activity • One number is to be selected from the set S = {1,2,3,4,5,6,7,8,9,10}. • Let A be the event: “the selected number is odd” • Let B be the event: “the selected number is a multiple of 3” • Find: the following events: A or B, A and B • Complement of A. Are A and B disjoint? Class Activity Select a card from an ordinary deck of 52 cards. Let A= the card is a black card B= the card is a picture card C = the card is an ace Describe the following events: A and B, B or C, A-complement Are B and C disjoint? Chapters 14 and 15 : Probability Mathematical Probability: Intuitively probability of an event is its...
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Chapters 14 and 15-1 - Ch 14 From randomness to Probability...

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