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# chapter5 - CHAPTER 5 PROBABILITY 5.1 What is probability...

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CHAPTER 5: PROBABILITY 5.1 What is probability? Random experiment results in one of a number of possible outcomes. The outcome that occurs cannot be predicted with certainty. Examples : Tossing a coin, rolling a die. Sample Space (S) - the list of all possible outcomes of a random experiment Experiment Sample Space Tossing a coin once S = {H, T} Rolling a die once S = {1,2,3,4,5,6} Tossing a coin twice S = {HH, HT, TH, TT} H=Head, T=Tail Example: Tossing a coin twice (tree diagrams) 1st toss 2nd toss Outcomes H H H H T H T T H T H T TT 1

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Event - any subset of a sample space Sample Space S Event A Examples: Experiment S Event Tossing a coin {H, T} Head is obtained = {H} Rolling a die {1,2,3,4,5,6} Number of dots is even ={2,4,6} Rolling a coin twice {HH, HT, TH, TT} The same outcome in both tosses ={HH, TT} P(A) -the probability of an event A 1. Relative frequency definition of probability: P(A) = the fraction of time the event A occurs in a long series of repetitions of a random experiment. Example: Experiment = tossing a fair coin, event A = head is obtained. Then P(A) = 0.50. 2
2. Classical definition of probability: If S consists of m equally likely outcomes, an event A

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chapter5 - CHAPTER 5 PROBABILITY 5.1 What is probability...

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