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Probability - Horton's "Roll up the Rim" contest

by Eleanor
(Canada)











































Tim Horton's "Roll up the Rim" contest states that you have a 1 in 9 chance of winning a prize. How many coffees would you have to buy to guarantee that you will be a winner? Explain fully

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May 19, 2010
Probability
by: Staff


The problem:

Tim Horton's "Roll up the Rim" contest states that you have a 1 in 9 chance of winning a prize.
How many coffees would you have to buy to guarantee that you will be a winner?
Explain fully

The solution


There can never be a guarantee of winning. There can never be a 100% chance of winning.

One might thing that by buying 9 coffees to play “Roll up the Rim” 9 times, they would have a 100% probability of winning.

Not true.

The purchase of each coffee has only a 1 in 9 chance of winning. It never gets any better than 1 in 9. One purchase does not influence your chance of winning with the next coffee purchase.

However, if you purchase every cup of coffee produced by the company in all of its outlets, you would have a 100% chance (a guarantee) that 1/9 of your coffee cup rims would produce a prize.

By the way, various corporations have been formed to buy up 100% of the lottery tickets sold in some lotteries. They do win since they have purchased all of the tickets.

As far as I know, this strategy has been used successfully in Australia and in some of the State Lotteries in the US. But . . . you must ensure you buy EVERY ticket.




Thanks for writing.


Staff
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