Problem 29 · 2017 Math Kangaroo
Stretch
Counting & Probability
Logic & Word Problems
caseworkcareful-counting
Three weights are randomly placed on each tray of a beam balance. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103, 104, 105 and 106 grams. For how many percent of the possible distributions is the 106-grams-weight on the right (heavier) side?
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Answer: B — 80 %
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Hint 1 of 2
List the splits of the six weights into two trays of three with the right side heavier.
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Hint 2 of 2
Among those, count how often the heaviest weight (106) is on the right.
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Approach: enumerate the heavier-right splits and check where 106 sits
- Of the C(6,3)=20 ways to fill the right tray, exactly half (10) make the right side heavier.
- Counting those, the 106-gram weight is on the right in 8 of the 10 cases.
- That is 8/10 = 80%, choice B.
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