## Lecture 9

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Stat 11 0 Lecture 9 Handout Chapter 3 3 3 4 Venn Diagrams pages 9 15 of the handout These diagrams are not required for the course but it may make some of the reading easier for those of you who struggle through this material There is also a link on the course webpage at http web stat ucla edu vlew stat11 lectures venn venn html 1 Postulates of probability formally pages 15 19 of the handout There are three basic rules of probability All other rules stem from proofs based on these three Postulate 1 The probability of any event must be a positive real number or zero symbolically P A 0 for any event A This basically means that you cannot have a negative probability event Postulate 2 The probability of a sample space is always 1 symbolically P S 1 for any sample space S So this means that the probability of some event from the sample space happening is certain This is why when we describe the sample space we must be exhaustive If we miss something that is possible the probability of something happening from the sample space will not be 1 or 100 Postulate 3 If the set of events A1 A2 A3 AN are mutually exclusive events the probability that one or the other will occur equals the sum of their respective probabilities symbolically P A1 A2 AN P A1 P A2 P AN for any N mutually exclusive events This could be rewritten as P A1 A2 AN n P A i i 1 Therefore suppose A1 A2 A3 are mutually exclusive then the probability of A1 or A2 or A3 happening is the sum of their respective probabilities Here s a table of 133 movies that grossed over 100 million dollars by quarter of opening day release date between 1996 2003 quarter Freq Percent Cum 1 10 7 52 7 52 2 48 36 09 43 61 3 34 25 56 69 17 4 41 30 83 100 00 Total 133 100 00 If we could pretend that this was a stable population we could apply some of the rules listed above and extensions to those rules Let s let 1 Jan 1 Mar 31 2 Apr 1 Jun 30 3 Jul 1 Sep 30 4 Oct 1 Dec 31 Example 1 2 Suppose you choose a 100 million dollar movie at random

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