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Examples of how to use the table: 1) In the 6/49 matrix, let us find the probability of occurrence of the same number exactly 15 times in 80 draws. In the table, we follow the intersection of row v = 15 with column t = 80 and we find the probability 0.02844 = 2.844%. 2) In the 6/49 matrix, let us find the probability of occurrence of the same number for a minimum of 8 times in 20 draws. In the table we follow the column t = 20 and add together all the values in this column standing between the rows v = 8 and v = 20 inclusive. We obtain: 0.001328 + 0.000247 + 3.79E-05 + 4.81E-06 + 5.03E-07 + 4.32E-08 + 3.02E-09 + 1.68E-10 + 7.34E-12 + 2.41E-13 + 5.6E-15 + 8.23E-17 + 5.74E-19 = 0.001618 = 0.1618% .............. missing part ................... In the same way, we can obtain calculus formulas for the probabilities of repeated events of any type – for example, for the repeated occurrence of more than 2 given numbers in the draws or events related to various numerical properties (consecutiveness, parity, divisibility, etc.). If we want to find the probability of a repeated event in several consecutive draws, we can use directly the formula from the definition of independent events (F7), applied several times successively: If the singular event A has probability u for one draw, then it occurs in each of t independent drawings (in particular, consecutive drawings) with probability ut . This result can be also obtained by choosing v = t in Bernoulli’s formula; therefore, it is a particular case of the results of this chapter. Example: In a 5/36 matrix, what is the probability of occurrence of the number 14 in 3 consecutive draws? For one draw, we have u = 0.138889 (according to the table from case a) of the event of occurrence of one single number). For 3 consecutive draws, the probability of occurrence of that number in all 3 draws will be u3 = 0.002679 0.268% . 62PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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