08_Ch5 - Ch. 5: (Probability) 5.1 (Definition) - an...

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Ch. 5: (Probability) 5.1 (Definition) - an experiment ( ): - a trial ( ): - a basic outcome / an elementary event / a simple event / a sample point( / ): . (ex) a, b, e1, e2, etc. - a sample space ( ): S . - An event or outcome ( / ): . (ex) A, E, F, W, E1, E2, etc, and we write E S, a F, etc. 0 1 : ( Probability is a measure, on a scale of zero to one, inclusive, of the chance of occurrence of an event, as determined by applying the appropriate choice from the following four definitions of probability:) 5.2 Classical definition of probability( ) - Suppose that an experiment can result in a finite number n of equally likely outcomes, and that k of these outcomes comprises a particular event E . Then the probability of event E , denoted by P(E) , is the ratio k/n , where 0 k/n 1, and we write P(E) = k/n . The classical definition is useful for many of our business related problems, but it cannot be used where there is an infinite number of possible outcomes or where the outcomes are not equally likely. Hence we need also the historically second definition: - . 2, 4, 6 E P(E) = k/n = 3/6 . Relative Frequency definition of probability( ) - If an event A occurs a times in m repetitions of an experiment, m A is called the (absolute) frequency of event A , m A /m is called the relative frequency of event A , and we have 0 m A /m 1. For smaller values of m, the values of m A /m fluctuate considerably, but for larger values of m , m A /m tends to stabilize about a specific number, P(A) , called the probability of event A , which is the limiting value of m A /m as m increases. Then for a larger values of m we may say P(A) = m A /m . The frequency definition of probability can be used to solve some of our business problems that the classical
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This note was uploaded on 10/28/2009 for the course BUSINESS 1 taught by Professor 1 during the Spring '09 term at Hanyang University.

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08_Ch5 - Ch. 5: (Probability) 5.1 (Definition) - an...

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