Beat the lottery Many states run lotteries to raise money. A website advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer several systems and criticize others as...

Beat the lottery Many states run lotteries to raise money. A website advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a “lucky” number to play, but maybe some numbers are luckier than others. Let’s use a simulation to see how well this system works. To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number. Pick a single value to bet, such as 1, and keep playing it over and over. You’ll want to run at least 100 trials. (If you can program the simulations on a computer, run several hundred. Or generalize the questions to a lottery that chooses two- or three-digit numbers—for which you’ll need thousands of trials.)

 a) What proportion of the time do you expect to win?

b) Would you expect better results if you picked a “luckier” number, such as 7? (Try it if you don’t know.) Explain.