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Chapter 4 OutlineDetermine sample spaces and find the probability of an event using classical probability or empirical probability.Find the probability of compound events using the addition rules.Find the probability of compound events using the multiplication rules.Find the conditional probability of an event.Determine the number of outcomes of a sequence of events using a tree diagram.Find the total number of outcomes in a sequence of events using the fundamental counting rule.Find the number of ways r objects can be selected from n objects using the permutation rule.Find the number of ways r objects can be selected from n objects without regard to order using the combination rule.Find the probability of an event using the counting rules.Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of insurance, investments, and weather forecasting, and in various areas.Rules such as the fundamental counting rule, combination rule and permutation rules allow us to count the number of ways in which events can occur.Counting rules and probability rules can be used together to solve a wide variety of problems.Basic ConceptsA probability experiment is a chance process that leads to well-defined results called outcomes.An outcome is the result of a single trial of a probability experiment.A sample space is the set of all possible outcomes of a probability experiment.An event consists of a set of outcomes of a probability experiment.Basic Concepts (cont'd.)Equally likely events are events that have the same probability of occurring.Venn diagrams are used to represent probabilities pictorially.Classical ProbabilityClassical probability uses sample spaces to determine the numerical probability that an event will happen.Classical probability assumes that all outcomes in the sample space are equally likely to occur.Rounding Rule for ProbabilitiesProbabilities should be expressed as reduced fractions or rounded to two or three decimal places. When the probability of an event is an extremely small decimal, it is permissible to round the decimal to the first nonzero digit after the decimal point.Probability Rules1. The probability of an event E is a number (either a fraction or decimal) between and including 0 and 1. This is denoted by:Rule 1 states that probabilities cannot be negative or greater than one.Probability Rules (cont'd.)2. If an event E cannot occur (i.e., the event contains no members in the sample space), the probability is zero.3. If an event E is certain, then the probability of E is 1.4. The sum of the probabilities of the outcomes in the sample space is 1.Complementary EventsThe complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by .Rule for Complementary EventsEmpirical ProbabilityEmpirical probability relies on actual experience to...

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