Beat the lottery Many states run lotteries to raise money.A Web site advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer sev-eral systems and criticize others as foolish. One system is called Lucky Numbers. People who play the LuckyNumbers system just pick a “lucky” number to play, butmaybe some numbers are luckier than others. Let’s use asimulation to see how well this system works.To make the situation manageable, simulate a simplelottery in which a single digit from 0 to 9 is selected asthe winning number. Pick a single value to bet, such as 1,and keep playing it over and over. You’ll want to runat least 100 trials. (If you can program the simulationson a computer, run several hundred. Or generalize thequestions to a lottery that chooses two- or three-digitnumbers—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’tknow.) Explain.
Beat the lottery Many states run lotteries to raise money.A Web site advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer sev-eral systems and criticize others as foolish. One system is called Lucky Numbers. People who play the LuckyNumbers system just pick a “lucky” number to play, butmaybe some numbers are luckier than others. Let’s use asimulation to see how well this system works.To make the situation manageable, simulate a simplelottery in which a single digit from 0 to 9 is selected asthe winning number. Pick a single value to bet, such as 1,and keep playing it over and over. You’ll want to runat least 100 trials. (If you can program the simulationson a computer, run several hundred. Or generalize thequestions to a lottery that chooses two- or three-digitnumbers—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’tknow.) Explain.
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Beat the lottery Many states run lotteries to raise money.
A Web site advertises that it knows “how to increase
A Web site advertises that it knows “how to increase
YOUR chances of Winning the Lottery.” They offer sev-
eral systems and criticize others as foolish. One system
eral 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.
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.
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