UASTAT151Ch5 - 5.1 Introducing Probability Defn: An...

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5.1 Introducing Probability Def’n: An experiment is a process that, when performed, results in one and only one of many observations. These observations are called the outcomes of the experiment. Probability is a numerical measure of likelihood that a specific outcome occurs. 3 Conceptual Approaches to Probability : 1) Classical probability - equally likely outcomes exist when two or more outcomes have the same probability of occurrence - classical probability rule : P ( A ) = (# of outcomes favourable to A ) / (total # of outcomes for experiment) 2) Relative frequency concept of probability - experiment repeated n times to simulate probability - relative frequencies are NOT probabilities, they only approximate them. - Law of Large Numbers : If an experiment is repeated again and again, the prob. of an event obtained from the relative frequency approaches the actual or theoretical prob. 3) Subjective probability - subjective probability is the degree of belief that an outcome will occur, based on the available information 5.2/5.3 Calculating Probability Def’n: A sample space (a.k.a. S ) is the set of all outcomes of an experiment. An event (a.k.a. A ) is a subset of elementary outcomes; . S A Æ P ( A ) = probability that A occurs A union of 2 events is denoted by A or B (or B A U ). An intersection of 2 events is denoted by A and B (or B A I ). A complement of an event is denoted by A C . A Venn diagram is a picture that depicts S (events above drawn in class). Experiment Outcomes Sample Space Toss a coin Head, Tail S = { H, T } Toss 2-headed coin Head S = { H } Toss a $5 bill Get it back, Lose money S = { Lucky, Not Smart } Pick a suit Spades, Clubs, Diamonds, Hearts
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UASTAT151Ch5 - 5.1 Introducing Probability Defn: An...

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