# Section4-2 - Basic Concepts of Probability A Bourhim...

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Basic Concepts of Probability A. Bourhim Syracuse University MAT121-Fall 2011 A. Bourhim (Syracuse University) Basic Concepts of Probability MAT121-Fall 2011 1 / 11
Rare Event Rule If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. Definition An outcome is the result of a single trial of an experiment. An event is one or more outcomes of an experiment. Any event which consists of a single outcome is called a simple event . The sample space is the list of all outcomes. Example A single 6-sided die is rolled. The possible outcomes of this experiment are: 1, 2, 3, 4, 5, 6. Rolling a single number (like 1 or 2) is a simple event. Rolling an even number is an event: 2, 4, 6. Rolling an odd number is an event: 1, 3, 5. Rolling a number large than 3 is an event: 4, 5, 6. A. Bourhim (Syracuse University) Basic Concepts of Probability MAT121-Fall 2011 2 / 11
Notation Events are denoted by A , B , C , ... Probability is the measure of how likely an event A is, and is denoted by P ( A ) . Rule 1 : Relative Frequency Approximation of Probability If an experiment is repeated n times and event A occurs s times, then the relative frequency of A approximates P ( A ) : P ( A ) s n . Example Suppose we toss a coin 50 times and have 27 heads and 23 tails . The relative frequency of heads is: 27 50 = 54 % .