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Problem

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problem

In an election for the Peer Pressure High School student council president, there are 2019 voters and two candidates Alice and Celia (who are voters themselves). At the beginning, Alice and Celia both vote for themselves, and Alice's boyfriend Bob votes for Alice as well. Then one by one, each of the remaining 2016 voters votes for a candidate randomly, with probabilities proportional to the current number of the respective candidate's votes. For example, the first undecided voter David has a 23\frac{2}{3} probability of voting for Alice and a 13\frac{1}{3} probability of voting for Celia. What is the probability that Alice wins the election (by having more votes than Celia)?
Plain-text mathematical notation (without MathML)
In an election for the Peer Pressure High School student council president, there are 2019 voters and two candidates Alice and Celia (who are voters themselves). At the beginning, Alice and Celia both vote for themselves, and Alice's boyfriend Bob votes for Alice as well. Then one by one, each of the remaining 2016 voters votes for a candidate randomly, with probabilities proportional to the current number of the respective candidate's votes. For example, the first undecided voter David has a (2)/(3) probability of voting for Alice and a (1)/(3) probability of voting for Celia. What is the probability that Alice wins the election (by having more votes than Celia)?
Original LaTeX notation
In an election for the Peer Pressure High School student council president, there are 2019 voters and two candidates Alice and Celia (who are voters themselves). At the beginning, Alice and Celia both vote for themselves, and Alice's boyfriend Bob votes for Alice as well. Then one by one, each of the remaining 2016 voters votes for a candidate randomly, with probabilities proportional to the current number of the respective candidate's votes. For example, the first undecided voter David has a $\frac{2}{3}$ probability of voting for Alice and a $\frac{1}{3}$ probability of voting for Celia. What is the probability that Alice wins the election (by having more votes than Celia)?

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Source and history

task_id
14e229fb-32d9-59b4-aa20-0a756339b1f5
task_key
test--14e229fb-32d9-59b4-aa20-0a756339b1f5
task_revision_id
1
config / split
/ test

Official source

initial import