Quote: Originally posted by RJOh on August 02, 2004
Quote: Originally posted by prob987 on August 01, 2004
Typically the sales figures for a $10,000,000 jackpot are around $11,000,000.
This corresponds to roughly a 92% chance of a rollover, roughly 1 in 23. Thus the results are consistent with the probabilities.
How does $11,000,000/135,145,920 possible combinations, 92% and 1:23 relate to results that are consistent with the probabilties?
RJOh
As always, I rely on my poisson spreadsheet to calculate probabilities. You will see though that 11,000,000/135,145,920 is very close to 0.08 or 8%, since there are very few double covered numbers when the ratio of sales to odds is small, and the simple ratio approximation is valid. I then attempted to reduce 8/92 by dividing the numerator and denominator by 4, which gives 2 to 23, not 1 to 23. Therefore I was wrong. I have to stop doing math in my head late at night. I think there's been about 20 ten million dollar jackpots since the Big Game became Mega Millions, so there should have, I guess, theoretically been two such jackpots hit. Maybe it will happen again soon.
Probabilities sometimes do not correspond to actual outcomes. If they did, no one would ever play the lottery.