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Chapter 4 Introduction to Probability

# Chapter 4 Introduction to Probability - Chapter 4...

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Chapter 4 – Introduction to Probability - Probability is a numerical measure of the likelihood that an event will occur. Probability values are always assigned on a scale from 0 to 1; a probability near zero indicates an event is unlikely to occur, and a probably near 1 indicates an event is almost certain to occur Experiments, Counting Rules, and Assigning Probabilities - An experiment is a process that generates well-defined outcomes. During the repetition of an experiment, one and only one of the possible experimental outcomes will occur - The sample space for an experiment is the set of all experimental outcomes - An experimental outcome is also referred to as a sample point to identify it as an element of the sample space Counting Rules, Combinations, and Permutation - The counting rule for multiple-step experiments can be expressed as: If an experiment can be described as a sequence of k steps with n 1 possible outcomes on the first step, n 2 on the second and so on, then the total number of experimental outcomes is given by (n 1 )(n 2 )…(n k ) - A tree diagram is a graphical representation that helps visualize a multiple-step experiment (Figure 4.2) - A second counting rule allows one to count the number of experimental outcomes when the experiment involves selecting n objects from a set of N objects (Equation 4.1 p. 145) - The notation ! means factorial; for example, 5 factorial is 5! = (5)(4)(3)(2)(1) = 120 -

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