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Unformatted text preview: 5 1 Chapter Five A Survey of Probability Concepts A Survey of Probability Concepts Objectives When you have completed this chapter, you will be able to: ONE Define probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREE Understand the terms: experiment, event, outcome, permutations, and combinations. 5 2 Chapter Five continued A Survey of Probability Concepts A Survey of Probability Concepts Objectives When you have completed this chapter, you will be able to: FOUR Define the terms: conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and the rules of multiplication. SIX Use a tree diagram to organize and compute probabilities. 5 3 Definitions Definitions A probability is a measure of the likelihood that an event in the future will happen. It it can only assume a value between 0 and 1. A value near zero means the event is not likely to happen. A value near one means it is likely. There are three definitions of probability: classical, empirical, and subjective. 5 4 Definitions Definitions continued continued The classical definition applies when there are n equally likely outcomes. The empirical definition applies when the number of times the event happens is divided by the number of observations. Subjective probability is based on whatever information is available. 5 5 Definitions Definitions continued continued An experiment is the observation of some activity or the act of taking some measurement. An outcome is the particular result of an experiment. An event is the collection of one or more outcomes of an experiment. 5 6 Mutually Exclusive Events Mutually Exclusive Events Events are mutually exclusive if the occurrence of any one event means that none of the others can occur at the same time. Events are independent if the occurrence of one event does not affect the occurrence of another. 5 7 Collectively Exhaustive Events Collectively Exhaustive Events Events are collectively exhaustive if at least one of the events must occur when an experiment is conducted. 5 8 A fair die is rolled once. The experiment is rolling the die. The possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. An event is the occurrence of an even number. That is, we collect the outcomes 2, 4, and 6. Example 1 Example 1 5 9 EXAMPLE 2 EXAMPLE 2 Throughout her teaching career Professor Jones has awarded 186 As out of 1,200 students. What is the probability that a student in her section this semester will receive an A?...
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 Spring '12
 Mohamed

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