It is also sometimes useful to refer to an event not

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Unformatted text preview: = E ∪ O = {2, 4, 6} ∪ {1, 3, 5} = Ω. Thus, P (EO) = 0 and P (E ∪ O) = 1. This makes sense, because the number that shows can’t be both even and odd, but it is always either even or odd. It is also sometimes useful to refer to an event not being true, which is equivalent to the complement of the event being true, where the complement of an event is the set of outcomes not 1 Here BE is the intersection of sets B and E. It is the same as B ∩ E. See Appendix 6.1 for set notation. 1.2. AXIOMS OF PROBABILITY 7 in the event. For example, the complement of B, written B c , is the event {3, 4, 5, 6}. Then, when the die is rolled, either B is true or B c is true, but not both. That is, B ∪ B c = Ω and BB c = ∅. Thus, whatever events we might be interested in initially, we might also want to discuss events that are intersections, unions, or complements of the events given initially. The empty set, ∅, or the whole space of outcomes, Ω, should be events, because they can naturally arise through taking comple...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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