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estimate of 4,364,023,663 for the number of tickets sold during this period. As a check on our estimate for n, we can calculate the expected number of each type of prize and see if these are reasonably close to the actual number of winners for each of the 9 prizes. The results of doing this are shown in Table 10. Prize 5+1 5 4+1 4 3+1 3 2+1 1+1 Expected 79 3493 15875 698509 619133 27,241,832 7,842,346 36,270,849 52,230,022 Observed 86 3551 15513 709,021 620,748 27,420,306 7,849,633 36,217,584 52,085,781 22 1 Table 10: Observed vs. expected number of prizes won. We see that the observed numbers fit the expected numbers quite well. Another check would be to see if the amount paid out is the same as the amount taken in. We have the following statement from the Powerball FAQ The Multi-State Lottery Association (which administers the PowerBall game) is a non-profit government-benefit association entirely owned and operated by the member state lotteries. PowerBall is a 50% prize payout game which means that 50 cents of every one dollar ticket is paid out in prizes. The state lottery keeps 50% as its share and then pays the rest out in prizes. The state lottery pays the cash prizes directly to the players in its state and then sends the percentage share for the jackpot prize back to the association where we hold it until there is a winner. The state that sells a ticket keeps ALL of the profit from that ticket. The only money that is sent to the central organization is the money to pay the jackpot prize. From this we see that the amount paid out should be 50% of the amount taken in. To find the amount paid out we have to remember that, for the jackpot, the lottery officials do not need the total amount of the jackpot. They indicate, for example, that for a 20 million dollar jackpot they only need 12 million dollars. Based on this, we have assumed that they need about 60% for any jackpot. If we use this, we find that the total prizes have cost the lottery a total of 2,192,892,845 dollars. Our estimate for the amount taken in (number of tickets sold) wasPDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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