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Chapter4

# Chapter4 - 4.1 Randomness Chapter 4 Probability the study...

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1 Chapter 4 Probability: the study of randomness (covered by about 3 lectures) 4.1: Randomness • Deterministic event – e.g. my car won’t run without gas • Example 1: random phenomena • Random events – The outcome is uncertain before it occurs. – There is a regular pattern for possible outcomes in a large number of repetitions . (not true for chaotic or haphazard events, such as earthquake). 4.2 Probability Models a list of possible outcomes. • a probability for each outcome.

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2 Sample space • Sample space S of a random phenomenon: the set of ALL possible outcomes. e.g. tossing a coin once S ={H, T} e.g. Do you favor mandatory retirement S ={Y,N} Event • Event: a set of outcomes of a random phenomenon. It is a subset of a sample space. e.g. toss a fair coin twice: Sample space S=? Event A: #heads=1 What outcomes this event includes? Sample space, outcome and event Toss a fair coin twice. S ={HH, HT, TH, TT} Outcomes: the 4 individual elements in S Event A: exactly one head occurs. A={HT, TH}, contains 2 outcomes Event B: at least one head occurs. B={HH, HT, TH}, contains 3 outcomes Note: for each toss, one and only one outcome occurs. Another example Toss a fair coin four times • Using a tree structure to exhaust all possible outcomes • Define the outcome as number of heads, sample space? Comment : the sample space depends on how we define individual outcome.
3 Probability rule P(A): the probability of event A occurs Rule 1 : Any probability is a number between 0 and 1 Rule 2 : All possible outcomes together must have probability 1. 0( ) 1 PA () 1 PS Venn Diagram: sample space X X X X X X X X X X X X X X X X X X X X X X X X X X Venn Diagram: An event

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4 Two events: case 1 Two events: case 2 Disjoint events
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Chapter4 - 4.1 Randomness Chapter 4 Probability the study...

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