(im)possible lottery outcome

Another outcry after an “impossible” lottery result that “must” be fraudulous! Obtaining the sequence 5,6,7,8,9,10 on the Tuesday December 1, 2020, draw of the Souht-African Powerball is indeed a low probability event. Just like obtaining any fixed sequence on a specific day for a specific lottery system. As I am unsure the last number has to differ from the others or not, consider the approximation where the 6 numbers are drawn uniformly without replacement from the first fifty integers. The number of outcomes is then approximately 16 millions, making any fixed outcome having a chance of 6 10⁻⁸ of happening for one draw. However, the psychological impact of an “impossible” lottery result would have been the same for any sequence of 6 consecutive numbers, which makes the event happening with a probability of approximately one chance in 400,000. Not so staggering then! And considering the repetition of lotteries, space- and time-wise, it takes roughly 40,000 draws for a consecutive sequence to be drawn with probability 10%. Which means 16 years if considering each US State having a draw every week…

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