PDF Publication Title:
Text from PDF Page: 031
From these three examples, the last gives the biggest difference of probability with the case of exclusive events, which is still very low. As in the first example, the numerical results of the last two remain the same whatever other numbers we choose, through a cyclic permutation of the 49 possible numbers (though not necessarily consecutive) of that matrix. We presented the complete solution of the three examples as both an exercise in probability calculus, and for seeing in a concrete case the evolution of the winning probability of a system when its constituent lines contain common numbers. The number of common numbers held by the simple lines taken two at a time can provide us with a sufficient condition for the events V k to be mutually exclusive, and implicitly, for the winning i probability of the system to increase proportionately with the number of played lines. One can see in the previous examples that even with only two lines, a direct calculation becomes difficult at a certain point for a person having no basic mathematical background. The direct application of formula (*) for aleatory systems with several lines is practically impossible and is not justified with respect to making decisions on choosing the simple lines, especially for the cases in which there exists the alternative of an approximation. Only a software program can perform such calculations in a short time. .............. missing part ................... This is the required sufficient condition, namely a maximal number cij : any two lines of the system will not contain more than 2k – n – 1 common numbers. If this condition is fulfilled, then events V k are mutually exclusive, and implicitly, all the intersections from the probability formula (*) are empty, so the probability of winning with minimum k numbers from at least one played line grows linearly with the number of played lines. From now on, we call the exclusiveness condition of the lines of the system the condition that events V k are mutually exclusive. Hence, we proved that a sufficient condition for the exclusiveness i 31 iPDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
PDF Search Title:
THE MATHEMATICS OF LOTTERY Odds, Combinations, SystemsOriginal File Name Searched:
9789731991115sample.pdfDIY PDF Search: Google It | Yahoo | Bing
Cruise Ship Reviews | Luxury Resort | Jet | Yacht | and Travel Tech More Info
Cruising Review Topics and Articles More Info
Software based on Filemaker for the travel industry More Info
The Burgenstock Resort: Reviews on CruisingReview website... More Info
Resort Reviews: World Class resorts... More Info
The Riffelalp Resort: Reviews on CruisingReview website... More Info
CONTACT TEL: 608-238-6001 Email: greg@cruisingreview.com (Standard Web Page)