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1. Dear Math Helper,
I am in need of your help! I have a job where I design games. I am designing a game that involves a playing area with 12 equal sections. Players randomly end up in one of the sections.
I labeled one section, "Gain 40 points," four sections, "Gain 10 points," and the rest, "Try Again." Also, each player automatically gives up 10 points with each move.
After trying out the game on some volunteers, I noticed that players tend to lose points in the long run. Without changing the sizes of the sections, what adjustments can I make so that players are likely to earn at least one point, in the long run?
Dear Game Maker,
Type your response here.
2. Dear Math Helper,
First, let me tell you how much I enjoy your column. It is the first thing I read in every issue.
I run a carpet cleaning company and need some advice. I want to offer steam cleaner rentals, because some people prefer to save money by cleaning their own carpets. But steam cleaners are expensive and they need repairs if not used properly, so I'm going to offer insurance policies. I'm not sure how much to charge.
It will cost me $190 to replace one of my cleaners, and repairs average $100. I talked to some other people I know in the business and they said I should expect to replace a cleaner for about 1 of every 50 rentals and to repair a cleaner for about 1 of every 20 rentals. I'm not sure what to do with all this information.
Please help me determine a fair price for my insurance policy. I want my rates to be low enough that customers buy the insurance, but high enough that I don't lose money by offering it. And please show me how you came up with your figure, so that I can make adjustments later if I need to.
Your number one fan,
Steaming in Seattle...