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Note 1 - Math 151 Probability Spring 2011 Jo Hardin...

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Math 151 – Probability Spring 2011 Jo Hardin Probability Rules Handout Probability Definitions The probability of an outcome refers to how often the outcome would occur in the long run if a random process were repeated over and over under identical conditions (relative frequency interpretation). An experiment is any activity or situation in which there is uncertainty about the outcome. The sample space is the list of all possible outcomes of a random trial. (Called S .) An event is any potential subset of the sample space. A simple event is an event consisting of exactly one outcome. Two events are mutually exclusive or disjoint if they cannot both occur simultane- ously. Two events are independent if the occurrence of one does not change the probability that the second will occur. Set Theory Consider three events. A : { woman has a tattoo } B : { someone age 18-29 has a tattoo } C : { someone has a tattoo } A C B C because both A and B are subsets of C Empty Set Is the set with no outcomes and is denoted: . Union The union of A and B is defined to be the event containing all outcomes that belong to A alone, to B alone, or to both A and B: A B . A B = B A A A = A A ∪ ∅ = A A S = S if A B A B = B A B C = ( A B ) C = A ( B C ) (associative) If we have n separate events, A 1 , A 2 , . . . , A n , A 1 A 2 ∪ · · · ∪ A n = n i =1 A i
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Intersection The intersection of A and B is defined as the events in both A and B: A B = AB .
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