To answer the first question, consider how the lottery changes for the public with the addition of the syndicate. To be specific, suppose the syndicate can invest $7 million and obtain all the possible tickets, making itself a sure winner. Also suppose, n people from the general public purchase tickets, each of which has 1 chance out of 7 million of being a winner. Finally let R be the jackpot carried over from any previous lotteries. Then the total jackpot on this round will be [R 0.39(7,000,000 n)] because 39 cents from every ticket goes towards the jackpot. The number of winning tickets for the public will be Poisson distributed with = n / 7,000,000. However, any member of the public who wins will necessarily have to share the jackpot with the syndicate, which is a sure winner. Use this information to calculate the expected amount the public will win