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. 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