Problem 11 · 2025 Math Kangaroo
Medium
Counting & Probability
careful-counting
In the picture you can see five different wheels of fortune. Each wheel of fortune is divided into equal-sized parts, but the number of parts is different. Anna spins all of the wheels of fortune. If a wheel of fortune stops at the arrow with a dark sector, she wins. Which of the wheels of fortune gives Anna the best chance of winning?
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Answer: A — 1
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Hint 1 of 2
On a fair wheel, the chance of winning is just the share of the wheel that is dark: dark sectors out of total sectors.
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Hint 2 of 2
Write each wheel’s chance as a fraction and see which fraction is biggest — a bigger dark share on a wheel with fewer pieces wins.
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Approach: compare the fraction of dark sectors
- Each wheel is split into equal parts, so the chance of stopping on dark is simply the fraction of the wheel that is dark.
- Wheel 1 has 2 dark sectors out of 8, which is 14 of the wheel; the others all turn out to be smaller dark shares (each less than a quarter, since they spread their dark sectors over more pieces).
- 14 is the largest dark share, so wheel 1 gives Anna the best chance, and the answer is (A) 1.
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