361.The Heaviest Weight's Side
★★★classical probabilityCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
We have 6 weights of mass grams. We randomly place 3 weights on each side of a scale. Find the probability that the side holding the 206-gram weight is heavier.
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Condition on which two weights join 206. The total is , so 206's side wins iff its trio sums to at least .
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