In Lottoland, there is a weekly lottery in which six (standard) numbers plus one bonus number are drawn from the numbers 1,…, 45. In addition to this, one color is randomly drawn out of six colors. On the lottery ticket, six numbers and one color must be chosen. The players use the computer for a random selection of the six numbers and the color. Each ticket costs $1.50. The number of tickets sold is about the same each week. The prizes are allotted as shown in the table. The jackpot begins with 4 million dollars; this is augmented each week by another half million dollars if the jackpot is not won. The lottery does not publish information regarding ticket sales and intake, but does publish a weekly listing in the newspaper of the number of winners for each of the six top prizes. The top six prizes from the table had 2, 10, 14, 64, 676, and 3,784 winners over the last 50 drawings. (a) Estimate the amount of the weekly intake. (b) Estimate the average number of weeks between jackpots being won and estimate the average size of the jackpot when it is won. (c) Estimate the percentage of the intake that gets paid out as prize money.
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