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Probabilities of Repeated Events All probabilities obtained thus far refer to events corresponding to the same probabilistic experiment, namely the drawing of the winning numbers in a single lotto game. We can also calculate probabilities of some events containing several drawings belonging to different games. These drawings, from a probability point of view, represent independent experiments. These probabilities provide useful information, especially for players who study the draw statistics as part of a personal strategy of choosing which numbers to play and/or whether to play the same numbers or groups of numbers repeatedly. Generally, moving from the probability of occurrence of an event in a singular game to the probability of its repeated occurrence in several games requires a simple calculation based on Bernoulli’s scheme (F8): Assume that t independent experiments (drawings) are performed. In each experiment, event A can occur with probability u. Then the probability for event A to occur exactly v times in the t experimentsis P (A)=Cvuv(1−u)t−v. v,t t Calculating the probability of the repeated event assumes knowing in advance the probability of the singular event, namely u. Next we present the probabilities of some particular repeated events, expressed through general formulas and accompanied by numerical examples for matrix 6/49. a) We consider the singular event A as being the occurrence in the draw of a certain number. According to the calculus formula from the hypergeometric Cn−1 scheme (F9), we have u = P(A) = m−1 . This is the probability that the chosen number will occur in a draw. The next table lists the numerical results of this formula for the various lottery matrices. 58 CmnPDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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