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The Probabilities of Winning with Simple Lines General formula of the winning probability A playing ticket contains one or more simple lines, grouped in compound lines or particular systems. The ticket is declared a winner if at least one of its simple lines is winning, that is, among its p numbers there exist a certain number of winning numbers ( n1 , n2 , , nq ), according to the rules of the winning categories of that lottery matrix. Thus, given a simple line, we are interested first in what the probability of winning is with this line in one of the winning categories of that matrix. Further, we deduce a more general formula, namely of the probability that among the n drawn numbers, there is a certain number of numbers of the played line. As readers will notice, we preserved all the denotations for the parameters of a lottery matrix mentioned in the section titled Parameters of the lottery matrices. Consider a played simple line. Let w ≤ p and let Aw be the event “exactly w numbers from the p given numbers are drawn.” We deduce now the general formula of the probability P( Aw ) . .............. missing part ................... 22PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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