benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Emily starts with an empty bucket. Every second, she either adds a stone to the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Emily starts with an empty bucket. Every second, she either adds a stone to the bucket or removes a stone from the bucket, each with probability 12\frac{1}{2}. If she wants to remove a stone from the bucket and the bucket is currently empty, she merely does nothing for that second (still with probability 12\frac{1}{2}). What is the probability that after 2017 seconds her bucket contains exactly 1337 stones?
Plain-text mathematical notation (without MathML)
Emily starts with an empty bucket. Every second, she either adds a stone to the bucket or removes a stone from the bucket, each with probability (1)/(2). If she wants to remove a stone from the bucket and the bucket is currently empty, she merely does nothing for that second (still with probability (1)/(2)). What is the probability that after 2017 seconds her bucket contains exactly 1337 stones?
Original LaTeX notation
Emily starts with an empty bucket. Every second, she either adds a stone to the bucket or removes a stone from the bucket, each with probability $\frac{1}{2}$. If she wants to remove a stone from the bucket and the bucket is currently empty, she merely does nothing for that second (still with probability $\frac{1}{2}$). What is the probability that after 2017 seconds her bucket contains exactly 1337 stones?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
69058323-1cd0-5140-a706-5039dfacad9f
task_key
test--69058323-1cd0-5140-a706-5039dfacad9f
task_revision_id
1
config / split
/ test

Official source

initial import