By Fazlollah M. Reza

ISBN-10: 0486682102

ISBN-13: 9780486682105

Info conception

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**Sample text**

Dare incompatible. A+B+C+···+D=U At least one of the events 0, . . , D must occur. DISCRETE SCHEMES WITHOUT MEMORY- A traveler has the choice of traveling by car, combination of the three for a particular trip. Define the sample space and express some of the events of interest. Solution. Let C, T, and P correspond to the fact of traveling by car, plane, respectively. The following events are self-explanatory. CTP CTP' C'I' C+T U - P traveling by car, train, and plane traveling by car and train but not by plane traveling by car and train (with or without plane) traveling by car, by train, or by car and train (mayor may not take the plane) not traveling by plane Example 2-10.

Each outcome is a point of the sample space. For example, the throw of an ordinary die may be considered as an experiment having six possible outcomes. With this experiment we associate a universal set containing six points, each corresponding to one of the outcomes of the experiment: {1,2,3,4,5,6} If the die is thrown twice, the sample space associated with the experiment contains 36 points corresponding to the following outcomes: 11 21 31 41 51 61 12 13 14 15 16 22 23 24 25 26 32 33 34 35 36 42 43 44 45 46 52 53 54 55 56 62 63 64 65 66 A sample space may be finite or infinite, if it contains a finite or an infinite number of points, respectively.

In this respect the formula of combinatorial analysis will be used. 22. What is the probability of a person having four aces in a bridge hand? Solution. The number of all possible different hands equals the combination of 13 from 52 cards. For the number of favorable cases one may think of first removing the four aces from the deck and then dealing all possible combinations of hands 9 by 9. The addition of the four aces to each one of these latter hands gives a favorable case. 10 ·11 ·12 ·13 11 48) (52) (9 : 13 = 49 .

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