"On October 1, 2022, something strange happened in the Philippines: 433 people won the jackpot in the local lottery. For this particular lotto, six numbers ranging in value from 1 to 55 were randomly selected, and the 433 winners all matched. Even more bizarre, when arranged in ascending order, the winning numbers were: 9, 18, 27, 36, 45 and 54. In other words, the winning numbers were multiples of 9 (9 1, 9 2, 9 3, etcetera)."
"When drawing numbers for the lottery, six numbers are chosen randomly from 55 possibilities, with no repeating numbers. The order the numbers are drawn in does not matter. We describe the number of possible combinations this process can result in as 55 choose 6. Which equals roughly 29 million. So the probability of these exact numbers being drawn is 1 in roughly 29 million. But every other possible outcome has a similar likelihood of around 1 in 29 million."
A Philippine lottery draw on October 1, 2022 produced winning numbers 9, 18, 27, 36, 45 and 54, and 433 people matched all six numbers. The six numbers are each multiples of 9, an unusual numeric pattern that drew international attention and accusations of suspicious behavior. The number of possible six-number combinations from 55 choices is 55 choose 6, roughly 29 million, making the chance of any particular six-number set about one in 29 million. Determining whether the outcome indicates fraud requires Bayesian methods and additional assumptions that extend beyond straightforward combinatorial probability.
Read at www.scientificamerican.com
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