ClassNotes-Chapter-04-v4-Appendix-1 - Sven Thommesen 2011...

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1 © Sven Thommesen 2011 CHAPTER 4 (v4 Appendix 1): Summary of the RULES OF PROBABILITY [Edited 09/23/08] DEFINITIONS 1. We will use the term probability to denote a numerical measure of likelihood , a measure that obeys certain rules: a) Let us use the notation P(x) or Pr(x) to mean “the probability that event x will happen.” b) P(x) ≥ 0 and P(x) ≤ 1: Our measure of probability is a (real) number between 0.0 and 1.0, inclusive. Mathematicians combine the two rules and write them this way: 0.0 ≤ P(x) ≤ 1.0 . c) If we say that “P(x) = 0” we mean either that event x cannot happen, or that we believe there is no chance whatsoever that it will happen. d) If we say that “P(x) = 1” we mean either that event x must happen, or that we believe that it is absolutely certain that it will. e) Other than those two extreme cases, for any other possible event we assign a probability between 0.0 and 1.0, larger the more likely the event is. f) If the probability that x will happen P(x) = 0.75, then the probability that x will NOT happen, P(not-x) , is equal to 1 P(x) = 1 0.75 = 0.25. [See Rule 4A below.] 2. Definition: a statistical experiment is an action or process that generates unique outcomes from a well-defined set of possible outcomes . (Imagine a black-box machine with a big red button on it; every time you hit the button, the machine randomly spits out one of the items it is capable of producing.) 3. We refer to each possible outcome of a statistical experiment as an elementary event ”. We call the set S of all possible outcomes for an experiment the “ sample space ” for that experiment. An eleme ntary event is sometimes referred to as a “ sample point ” (i.e. a point in the sample space). We refer to sample point #i as “e i ”.
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2 4. Sometimes we are interested in the probability that
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ClassNotes-Chapter-04-v4-Appendix-1 - Sven Thommesen 2011...

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