THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems

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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ( the-mathematics-lottery-odds-combinations-systems )

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.............. missing part ................... Below we present a separate table for the Keno game, in which 20 numbers are drawn from 80, and the playing lines can contain between4and20numbers(m=80,n=20, p∈{4,5,,20}). The formula of the winning probability becomes Cw ⋅C20−w P( A ) = p 80− p , which returns the following numerical values. w C20 80 In the table, in the first column are noted the values for w, and in the first row, the values for p. The existence of a dash indicates that such a case is impossible. .............. missing part ................... Examples of how to use the tables: In the 6/49 matrix, what is the probability of occurrence of 2 specific numbers from the played 6 in a draw? We search in the table corresponding to n = 6, at the intersection of row m = 49 with column w = 2 and we find the value 0.132378, that is 13.23%. In a 3/90 matrix, what is the probability of occurrence of 3 specific played numbers in a draw? We search in the table corresponding to n = 3, at the intersection of row m = 90 with column w = 3 and we find the value 8.51E-06, that is 0.00000851, and as percentage 0.000851%. In a Keno game, what is the probability of occurrence of 7 specific numbers from 17 played numbers in a draw? We search in the table corresponding to Keno, at the intersection of row w = 7 with column p = 17 and we find the value 0.057588, that is 5.75%. A quick perusal of the numerical results in the tables in this section indicates that most of the probabilities are very low, some of them very close to zero, including those specific to the winning categories. For example, in the 5/55 matrix, the occurrence of 3 numbers has the probability 0.35%, the occurrence of 4 numbers has 0.0719%, 26

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