Chapter 5 - A survey of probability concepts. In this chapter, the learning objectives are: Define probability; describe the classical, empirical, and subjective approaches to probability; explain the terms experiment, event, outcome, permutations, and combinations; define the terms conditional probability and joint probability; calculate probabilities using the rules of addition and rules of multiplication. | A Survey of Probability Concepts Chapter 5 GOALS Define probability. Describe the classical, empirical, and subjective approaches to probability. Explain the terms experiment, event, outcome, permutations, and combinations. Define the terms conditional probability and joint probability. Calculate probabilities using the rules of addition and rules of multiplication. Apply a tree diagram to organize and compute probabilities. Calculate a probability using Bayes’ theorem. Probability, Experiment, Outcome, Event: Defined PROBABILITY A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur. An experiment is a process that leads to the occurrence of one and only one of several possible observations. An outcome is the particular result of an experiment. An event is the collection of one or more outcomes of an experiment. Mutually Exclusive Events and Collectively Exhaustive Events Events are mutually exclusive if . | A Survey of Probability Concepts Chapter 5 GOALS Define probability. Describe the classical, empirical, and subjective approaches to probability. Explain the terms experiment, event, outcome, permutations, and combinations. Define the terms conditional probability and joint probability. Calculate probabilities using the rules of addition and rules of multiplication. Apply a tree diagram to organize and compute probabilities. Calculate a probability using Bayes’ theorem. Probability, Experiment, Outcome, Event: Defined PROBABILITY A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur. An experiment is a process that leads to the occurrence of one and only one of several possible observations. An outcome is the particular result of an experiment. An event is the collection of one or more outcomes of an experiment. Mutually Exclusive Events and Collectively Exhaustive 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 collectively exhaustive if at least one of the events must occur when an experiment is conducted. The sum of all collectively exhaustive and mutually exclusive events is (or 100%) Events are independent if the occurrence of one event does not affect the occurrence of another. collectively exhaustive and mutually exclusive events Classical and Empirical Probability Consider an experiment of rolling a six-sided die. What is the probability of the event “an even number of spots appear face up”? The possible outcomes are: There are three “favorable” outcomes (a two, a four, and a six) in the collection of six equally likely possible outcomes. The empirical approach to probability is based on what is called the law of large numbers. The key to establishing probabilities empirically is that more observations will provide a more accurate estimate of the probability. EXAMPLE: On February
