Chapter 2 Chapter 2.1-2.2 The sample space of an experiment, denoted S , is the set of all possible outcomes of that experiment. An event is any collection.

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Presentation transcript:

chapter 2 Chapter 2.1-2.2 The sample space of an experiment, denoted S , is the set of all possible outcomes of that experiment. An event is any collection (subset) of outcomes contained in the sample space S. An event is simple if it consists of exactly one outcome and compound if it consists of more than one outcome Ch2.1-2.2 2.1-2.2

Relations from Set Theory chapter 2 Relations from Set Theory The union of two events A and B is the event consisting of all outcomes that are in either A or B. Notation: Read: A or B 2. The intersection of two events A and B is the event consisting of all outcomes that are in both A and B. Notation: Read: A and B The complement of an event A is the set of all outcomes in S that are not contained in A. Notation: Read: A complement Ch2.1-2.2 2.1-2.2

Mutually Exclusive When A and B have no outcomes in common, they are mutually exclusive or disjoint events Ch2.1-2.2

chapter 2 Venn Diagrams A B A B A Ch2.1-2.2 2.1-2.2

If all Ai’s are mutually exclusive, then Axioms of Probability If all Ai’s are mutually exclusive, then (finite set) (infinite set) Ch2.1-2.2

Properties of Probability For any event A, If A and B are mutually exclusive, then For any two events A and B, Ch2.1-2.2

Example The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.4, the analogous probability for the second signal is 0.5 and the probability that he must stop at least one of the two signals is 0.6. What is the probability that he must stop At both signals? At the first signal but not the second one? At exactly one signal? Ch2.1-2.2