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Omni-MATH / There are 100 people standing in a line from left to right. Half of them are…

Problem

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problem

There are 100 people standing in a line from left to right. Half of them are randomly chosen to face right (with all $\binom{100}{50}$ possible choices being equally likely), and the others face left. Then, while there is a pair of people who are facing each other and have no one between them, the leftmost such pair leaves the line. Compute the expected number of people remaining once this process terminates.
Plain-text mathematical notation (without MathML)
There are 100 people standing in a line from left to right. Half of them are randomly chosen to face right (with all $\binom{100}{50}$ possible choices being equally likely), and the others face left. Then, while there is a pair of people who are facing each other and have no one between them, the leftmost such pair leaves the line. Compute the expected number of people remaining once this process terminates.
Original LaTeX notation
There are 100 people standing in a line from left to right. Half of them are randomly chosen to face right (with all $\binom{100}{50}$ possible choices being equally likely), and the others face left. Then, while there is a pair of people who are facing each other and have no one between them, the leftmost such pair leaves the line. Compute the expected number of people remaining once this process terminates.

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Source and history

task_id
fa06a2f2-1e19-54f9-baf3-158144fe1999
task_key
test--fa06a2f2-1e19-54f9-baf3-158144fe1999
task_revision_id
1
config / split
/ test

Official source

initial import