Which side holds the heavy weight

EasyProbability Combinatorics~4m

Six weights of masses $201, 202, \dots, 206$ grams are split at random, three to each pan of a balance. What is the probability that the pan containing the $206$ -gram weight is the heavier pan?

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The $206$ -pan is heavier iff its total exceeds half of $1221$ , i.e. its two companions sum to $\ge 405$ .
Count the $\binom{5}{2}=10$ companion-pairs; only $\{201,202\}$ and $\{201,203\}$ fall short.

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Asked at: Optiver, Akuna Capital

Which side holds the heavy weight

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