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Omni-MATH / Alice writes 1001 letters on a blackboard, each one chosen independently and…

Problem

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problem

Alice writes 1001 letters on a blackboard, each one chosen independently and uniformly at random from the set S={a,b,c}S=\{a, b, c\}. A move consists of erasing two distinct letters from the board and replacing them with the third letter in SS. What is the probability that Alice can perform a sequence of moves which results in one letter remaining on the blackboard?
Plain-text mathematical notation (without MathML)
Alice writes 1001 letters on a blackboard, each one chosen independently and uniformly at random from the set S={a,b,c}. A move consists of erasing two distinct letters from the board and replacing them with the third letter in S. What is the probability that Alice can perform a sequence of moves which results in one letter remaining on the blackboard?
Original LaTeX notation
Alice writes 1001 letters on a blackboard, each one chosen independently and uniformly at random from the set $S=\{a, b, c\}$. A move consists of erasing two distinct letters from the board and replacing them with the third letter in $S$. What is the probability that Alice can perform a sequence of moves which results in one letter remaining on the blackboard?

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Source and history

task_id
540394cf-49fb-52f4-8e21-b836ce8c5feb
task_key
test--540394cf-49fb-52f4-8e21-b836ce8c5feb
task_revision_id
1
config / split
/ test

Official source

initial import