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4,364,023,663. Thus our estimate would say that the lottery has paid out 50.2% of the amount they have taken in. This is pleasantly close to the 50% that the lottery officials aim for. It appears that the whims of fate even suggest that the percentage should be slightly larger than 50%. Here is what the lottery officials themselves say on their FAQ about how they have done. Have you had to pay more or less than what you expected statistically since the start of Powerball? Darin H., via Internet. The players have been luckier than the game design says they should be. To date (April 24, 1996), we have paid out $14,050,085 in "extra" prize money to winners - that is, prizes above what we would expect to pay out if people would pay more attention to the statistics. The total prizes paid out to date is over $722 million, so the difference is not significant (unless it is your $14 million!). OTHER LOTTERIES POSE NEW QUESTIONS There are many other interesting questions that can be explored about lotteries. The questions that one asks depend, to some extent, on the nature of the lottery. For example, in September 1996 the Multi-State lottery introduced a new lottery called Daily Millions where the amount of the jackpot is always $1 million dollars and, if you win, you don't have to share it with another person who also has the same winning pick (actually, if there are more than 10 such winners they share a 10 million dollar prize.) Here is an article from Chance News raising problems about this lottery. Daily Millions beats odds: no one wins -- 5-month losing streak puzzles even statisticians. Star Tribune, 7 Feb. 1997, 1B Pat Doyle The Daily Millions lottery was started nearly five months ago and at the time of this article, 34 million tickets had been sold without a single $1 million jackpot. It is stated that one would expect 3 or 4 winners by now and the probability of having no winners in this period is put at 1/38. The Daily Millions lottery is run by Multi-State Lottery Association which also runs the Powerball lottery. The Daily Millions was invented to give a lottery where you are do not 23PDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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