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Chapter 14 - Chapter 14 Read From Randomness to Probability...

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Chapter 14 From Randomness to Probability ActivStats: 14 Read: Chapter 14 Probability deals with modeling of random phenomena (phenomena or experiments whose outcomes may vary) Examples: 1. A toss of a coin 2. A roll of a die 3. A random selection of an individual from a population Intuitively probability of an event is a long-run relative frequency of the event in many independent repetitions of the experiment. Law of Large Numbers : ) ( # # A P s repetition of occured has A times of
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Model of a random phenomenon 1. The sample space S (or ) = the set of all possible outcomes 2. Events = subsets of the sample space Venn Diagram: If A is an event, the event that "A does not occur" is denoted A c and is called the complement of A Two events are called disjoint , if they cannot occur simultaneously Combined events: A and B, A or B A and B A or B A A B Union of A and B Union of A and B A C A
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4. Probability = a function that to each event A assigns a number P(A) (called the probability of an event A ) with the properties that 5. a) 0 P(A) 1 b) P(S) = 1 c) P(A c ) = 1- P(A) d) if A are B are disjoint, then P(A or B) = P(A) + P(B)
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