In Virginia's six-number lottery (or lotto) players pick six numbers from 1 to 44. The winning combination is determined by a machine that looks like a popcorn machine, except that it is filled with numbered table-tennis balls. The 'Virginia lottery drawing offered the prizes shown in Table STI 2.1, assuming that the first prize is not shared with a ticket price of $1. Common among regular lottery players is this dream: waiting until the jackpot reaches an astronomical sum and then buying every possible number, thereby guaranteeing a winner. Sure, it would cost millions of dollars, but the payoff would be much greater. Is it worth trying? How do the odds of umning the first prize change as you increase the number of tickets purchased?
Table STI 2.1

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Number of Prizes Prize Category First prize Second prizes ($899 each) Third prizes ($51 each) Fourth prizes (SI each) Total winnings Total Amount $27,007,364 204.972 538,152 168.073 $27,918,561 228 10,552 168,073