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slides3 - Lecture Stat 302 Introduction to Probability...

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Lecture Stat 302 Introduction to Probability - Slides 3 AD Jan. 2010 AD () Jan. 2010 1 / 8
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Sample Space De°nition . The sample space S of an experiment (whose outcome is uncertain) is the set of all possible outcomes of the experiment. Example (child): Determining the sex of a newborn child in which case S = f boy , girl g . Example (horse race): Assume you have an horse race with 12 horses. If the experiment is the order of °nish in a race, then S = f all 12 ! permutations of ( 1 , 2 , 3 , ..., 11 , 12 ) g . Example (coins): If the experiment consists of ±ipping two coins, then the sample space is S = f ( H , H ) , ( H , T ) , ( T , H ) , ( T , T ) g . Example (lifetime): If the experiment consists of measuring the lifetime (in years) of your pet then the sample space consists of all nonnegative real numbers: S = f x ; 0 ° x < g . AD () Jan. 2010 2 / 8
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Events Any subset E of the sample space S is known as an event ; i.e. an event is a set consisting of possible outcomes of the experiment. If the outcome of the experiment is in E , then we say that E has occurred. Example (child): The event E = f boy g is the event that the child is a boy. Example (horse race): The event E = f all outcomes in S starting with a 7 g is the event that the race was won by horse 7.
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