benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / In-Young generates a string of B zeroes and ones using the following method:

Problem

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

problem

In-Young generates a string of BB zeroes and ones using the following method: - First, she flips a fair coin. If it lands heads, her first digit will be a 0, and if it lands tails, her first digit will be a 1. - For each subsequent bit, she flips an unfair coin, which lands heads with probability AA. If the coin lands heads, she writes down the number (zero or one) different from previous digit, while if the coin lands tails, she writes down the previous digit again. What is the expected value of the number of zeroes in her string?
Plain-text mathematical notation (without MathML)
In-Young generates a string of B zeroes and ones using the following method:
- First, she flips a fair coin. If it lands heads, her first digit will be a 0, and if it lands tails, her first digit will be a 1.
- For each subsequent bit, she flips an unfair coin, which lands heads with probability A. If the coin lands heads, she writes down the number (zero or one) different from previous digit, while if the coin lands tails, she writes down the previous digit again.

What is the expected value of the number of zeroes in her string?
Original LaTeX notation
In-Young generates a string of $B$ zeroes and ones using the following method:
- First, she flips a fair coin. If it lands heads, her first digit will be a 0, and if it lands tails, her first digit will be a 1.
- For each subsequent bit, she flips an unfair coin, which lands heads with probability $A$. If the coin lands heads, she writes down the number (zero or one) different from previous digit, while if the coin lands tails, she writes down the previous digit again.

What is the expected value of the number of zeroes in her string?

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
0396e42d-c511-5680-b42e-8b9eacc51d04
task_key
test--0396e42d-c511-5680-b42e-8b9eacc51d04
task_revision_id
1
config / split
/ test

Official source

initial import