probability set up - 2 The probability set-up We will have...

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2. The probability set-up. We will have a sample space, denoted S (sometimes Ω) that consists of all possible outcomes. For example, if we roll two dice, the sample space would be all possible pairs made up of the numbers one through six. An event is a subset of S . Another example is to toss a coin 2 times, and let S = { HH, HT, TH, TT } ; or to let S be the possible orders in which 5 horses finish in a horse race; or S the possible prices of some stock at closing time today; or S = [0 , ); the age at which someone dies; or S the points in a circle, the possible places a dart can hit. We use the following usual notation: A B is the union of A and B and denotes the points of S that are in A or B or both. A B is the intersection of A and B and is the set of points that are in both A and B . denotes the empty set. A B means that A is contained in B and A c is the complement of A , that is, the points in S that are not in A . We extend the definition to have n i =1 A i is the union of A 1 , · · · , A n , and similarly n i =1 A i . An exercise is to show that ( n i =1 A i ) c = n i =1 A c i and ( n i =1 A i ) c = n i =1 A c i . These are called DeMor- gan’s laws.
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