PPT-Review of Probability

Jake Blanchard Spring 2010 Uncertainty Analysis for Engineers 1 Introduction Interpretations of Probability Classical If an event can occur in N equally likely and different ways and if n of these have an attribute A then the probability of the occurrence of A denoted PrA is defined as nN. AS91585. The language of probability questions. .. Section One. The question, "Do you smoke?" was asked of 100 people. . .. Yes. No. Total. Male. 19. 41. 60. Female. 12. 28. 40. Total. 31. 69. 100. The results are shown in the table.. Sections 4.7, 4.8: Poisson and . Hypergeometric. Distributions. Jiaping. Wang. Department of Mathematical Science . 03/04/2013, Monday. Outline. Poisson: Probability Function. . Poisson: Mean and Variance. Coins game. Toss 3 coins. You win if . at least two . come out heads. S. = { . HHH. , . HHT. , . HTH. , . HTT. , . T. HH. , . T. HT. , . T. TH. , . T. TT. }. equally likely outcomes. W. = { . HHH. Section 5.1. An event is the set of possible outcomes. Probability is between 0 and 1. The event A has a complement, the event not A. Together these two probabilities sum 1.. . ex. At least one and none are complements. Random Variables. Definition:. A rule that assigns one (and only one) numerical value to each simple event of an experiment; or. A function that assigns numerical values to the possible outcomes of an experiment.. calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) . Pr. (g). (disjunction rule) If h and g are . Probability Terminology. Classical Interpretation. : Notion of probability based on equal likelihood of individual possibilities (coin toss has 1/2 chance of Heads, card draw has 4/52 chance of an Ace). Origins in games of chance.. 4. Introduction. (slide 1 of 3). A key . aspect of solving real business problems is dealing appropriately with uncertainty.. This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty.. Conditional Probability. Conditional Probability: . A probability where a certain prerequisite condition has already been met.. Conditional Probability Notation. The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. A jar contains 10 purple marbles and 2 red marbles. If two marbles are chosen at random with no replacement, what is the probability that 2 purple marbles are chosen? . A bag contains 6 cherry, 8 strawberry, and 9 grape-flavored candies. What is the probability of selecting a cherry or a grape-flavored candy?. Mixture of Transparencies created by:. Dr. . Eick. and Dr. Russel. Reasoning and Decision Making Under Uncertainty. Quick Review Probability Theory . Bayes’ Theorem and Naïve Bayesian Systems. Bayesian Belief Networks.