One of the reasons why the Powerball Lottery (offered by 42 states, the U.S. Virgin Islands, and the District of Columbia) is so large is that the odds of winning are so small and the pot continues to grow until someone wins. To win the Powerball Jackpot, a player’s 5 game balls and 1 red powerball must match those chosen. Since Powerball began on April 19, 1992, the game has been changed. Each change has lowered the probability of winning by placing more balls in play. See the table, which compares the original and the 2011 powerball games.
Assume that a share of the Jackpot is $20 million, and find the expected winnings from one ticket in the original game and in the 2011 game. The sponsors of the Powerball game claim that making the probability lower improves the game. How do they justify that claim?
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