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Section 10.1

Section 10.1. Introduction to Probability. Probability. Probability is the overall likelihood that an event can occur. A trial is a systematic opportunity for an event to occur. An experiment is one or more trials conducted.

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Section 10.1

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  1. Section 10.1 Introduction to Probability

  2. Probability • Probability is the overall likelihood that an event can occur. • A trial is a systematic opportunity for an event to occur. • An experiment is one or more trials conducted. • A sample space is the set of all possible outcomes of an event. • An event is an individual outcome or any specified combination of outcomes.

  3. Probability • Probability is expressed as a number from 0 to 1, inclusive. • It is often written as a fraction, decimal, or percent. • An impossible event has a probability of 0. • An event that will always occur has a probability of 1. • The sum of the probabilities of all outcomes in a sample space is 1. • Outcomes are random if all possible outcomes are equally likely.

  4. Experimental and Theoretical Probabilities • Experimental (inductive) probability is approximated by performing trials and recording the ratio of the number of occurrences of the event to the number of trials. • Theoretical (deductive) probability is based on the assumption that all outcomes in the sample space occur randomly.

  5. Theoretical Probability • If all outcomes in a sample space are equally likely, then the theoretical probability of even A, denoted P(A), is defined by: • P(A) = number of outcomes in event A number of outcomes in the sample space

  6. Fundamental Counting Principle • If there are m ways that one event can occur and n ways that another event can occur, then there are m x n ways that both events can occur.

  7. Section 10.2 Permutations

  8. Permutations • A permutation is an arrangement of objects in a specific order. • When objects are arranged in a row, the permutation is called a linear permutation. • Permutations of n Objects: The number of permutations of n objects is given by n!. • If n is a positive integer, then n factorial, written n!, is defined as follows: • n! = n x (n – 1) x (n – 2) x (n – 3) x ··· x 2 x 1

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