handout4 - Chapter 4: Probability Bin Wang...

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Unformatted text preview: Chapter 4: Probability Bin Wang bwang@jaguar1.usouthal.edu Department of Mathematics and Statistics University of South Alabama Mann E6 1/29 4.1 Experiment, Outcome, and Sample Space Definition An experiment is a process that, when performed, results in one and only one of many observations. These observations are called the outcomes of the experiment. The collection of all outcomes for an experiment is called a sample space . Example Tossing a fair coin. Venn diagram and tree diagram. Example Tossing two fair coins. Mann E6 2/29 Mann E6 3/29 Mann E6 4/29 Notes Notes Notes Notes Mann E6 5/29 Mann E6 6/29 Mann E6 7/29 4.1.1 Simple and Compound Events Definition An event is a collection of one or more of the outcomes of an experiment. Definition An event that includes one and only one of the (final) outcomes for an experiment is called a simple event and is usually denoted by E i . Example (Tossing two fair coins) Find simple events in this experiment. Definition A compound event is a collection of more than one outcome for an experiment. Mann E6 8/29 Notes Notes Notes Notes Mann E6 9/29 4.2 Calculating Probability Definition Probability is a numerical measure of the likelihood that a specific event will occur. Two properties of Probability 1 P ( E i ) 1 0 P ( A ) 1 2 For an experiment: X P ( E i ) = P ( E 1 ) + P ( E 2 ) + = 1 . For the experiemnt of one toss of a coin, P ( H ) + P ( T ) = 1 , or P ( H ) = 1- P ( T ) . Mann E6 10/29 4.2.1 Three Conceptual Approaches to Probability (1) Classical Probability Definition Two or more outcomes that have the same probability of occurence are said to be equally likely outcomes....
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handout4 - Chapter 4: Probability Bin Wang...

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