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Here is a table of these probabilities for the different values of the number of tickets sold. Millions of tickets sold 10 20 30 40 50 60 70 Probability no one wins .834 .695 .579 .483 .403 .336 .280 21 Table 8: Probability no one wins the jackpot. From these we might be able to make a reasonable model where the probability that a head turns up each time increases after each tail. ESTIMATING THE TOTAL NUMBER OF TICKETS SOLD From the Multi-State Lottery homepage, we find the number of winners for all the prizes during this time period. (There are times when the prizes are doubled as a promotional feature.) Match 5+1 5 4+1 4 3+1 3 2+1 1+1 0+1 Total Prize Winners millions 86 $100,000 3540 Double winners Total winners Amount won $2,206,159,204 356,200,000 77,815,000 71,120,300 62,266,400 137,528,405 39,368,760 72,654,922 52243536 $3,075,356,527 86 3,551 $5000 15,463 50 15,513 $100 706,839 2,182 $100 618,832 1,916 $5 27,334,931 85,375 $5 7,825,514 24,119 $2 36,107,707 109,877 $1 51,928,026 157,755 709,021 620,748 27,420,306 7,849,633 36,217,584 52,085,781 124,922,137 0 11 Table 9: The prizes won up to March 1, 1997. An important bit of information we do not find on the Lottery’s web page is the total number of tickets sold. However, we can estimate this from the information we have. We know the probability of winning each prize from Table 4. Adding these we find the probability of winning at least one prize to be p = .0286. From Table 9 we see that the total number of people who won a prize in the first 508 drawings was w = 124,922,137. If n tickets were sold then we would expect w to be approximately np. Thus we can estimate n by w/p. This gives anPDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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