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Preliminaries and Introduction to Probability CEE 11 Spring 2002 Dr. Amelia Regan TA Riju Lavanya Preliminaries The syllabus and other important information for this class is posted on the eee server at eee.uci.edu. Several unannounced quizzes will be held on Tuesdays This course package contains a summary of the notes for each topic covered. Preliminaries Calculators with statistical functions are fine for getting the job done -- not for learning probability No calculators are allowed in the midterm Probability An informal definition of probability is a numerical value or the “chance” of occurrence of several possible outcomes of an unpredictable event. Engineers study probability because uncertainties are unavoidable in the design and planning of engineering systems Probability Understanding probability and statistics is also important for getting along in the world for understanding business reports, claims found in newspaper articles etc. for being able to distinguish between “coincidences that are likely and those that are not. Studying probability helps to gain intuition into mathematical modeling -- and to understand when intuition is likely to fail Several counter intuitive examples follow An example How many people would we have to gather in a room to be sure that at least two of them share the same birthday? Answer: 367 (don’t forget feb 29th) How many people would we have to gather in a room so that the chance that two of them have the same birthday is 50%? Answer: 23 Solution The probability that two people in a room do not have the same birthday is 365 364 365 365 The probability that five people in a room do not have the same birthday is 365 364 363 362 361 365 365 365 365 365 Solution We simply subtract these probabilities from 1.0 to get the complementary probability that if 2,3,…n people are in a room that at least two have the same birthday For n = 23 the probability is ~ 0.507 For n = 50, the approximate size of this class, the probability is 0.97