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Chapter 3: The basic concepts of probability

Chapter 3: The basic concepts of probability Experiment: a measurement process that produces quantifiable results ( throwing two dice, dealing cards, at poker, measuring heights of people, recording proton-proton collisions) Outcome: a single result from a measurement ( the numbers shown on the two dice) Sample space: the set of all possible outcomes from an experiment ( the set of all possible five-card hands) The number of all possible outcomes may be (a) finite ( all possible outcomes from throwing a single die; all possible 5-card poker hands) (b) countably infinite ( number of proton-proton events to be made before a Higgs boson event is observed) or (c) constitute a continuum ( heights of people) In case (a), the sample space is said to be finite in cases (a) and (b), the sample space is said to be discrete in case (c), the sample space is said to be continuous In this Chapter we consider discrete, mainly finite, sample spaces An event is any subset of a sample set (including the em)

The classical definition of probability If there are m outcomes in a sample space, and all are equally likely of being the result of an experimental measurement, then the probability of observing an event that contains s outcomes is given by e.g. Probability of drawing an ace from a deck of 52 cards. sample space consists of 52 outcomes.

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