benchmarks.wiki / Public workspace
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Omni-MATH / A certain lottery has tickets labeled with the numbers 1,2,3,…,1000. The lottery is run as follows: First, a ticket is drawn at random. If the number on the ticket is odd, the draw…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
A certain lottery has tickets labeled with the numbers . The lottery is run as follows: First, a ticket is drawn at random. If the number on the ticket is odd, the drawing ends; if it is even, another ticket is randomly drawn (without replacement). If this new ticket has an odd number, the drawing ends; if it is even, another ticket is randomly drawn (again without replacement), and so forth, until an odd number is drawn. Then, every person whose ticket number was drawn (at any point in the process) wins a prize. You have ticket number 1000. What is the probability that you get a prize?
Plain-text mathematical notation (without MathML)
A certain lottery has tickets labeled with the numbers 1,2,3,…,1000. The lottery is run as follows: First, a ticket is drawn at random. If the number on the ticket is odd, the drawing ends; if it is even, another ticket is randomly drawn (without replacement). If this new ticket has an odd number, the drawing ends; if it is even, another ticket is randomly drawn (again without replacement), and so forth, until an odd number is drawn. Then, every person whose ticket number was drawn (at any point in the process) wins a prize. You have ticket number 1000. What is the probability that you get a prize?
Original LaTeX notation
A certain lottery has tickets labeled with the numbers $1,2,3, \ldots, 1000$. The lottery is run as follows: First, a ticket is drawn at random. If the number on the ticket is odd, the drawing ends; if it is even, another ticket is randomly drawn (without replacement). If this new ticket has an odd number, the drawing ends; if it is even, another ticket is randomly drawn (again without replacement), and so forth, until an odd number is drawn. Then, every person whose ticket number was drawn (at any point in the process) wins a prize. You have ticket number 1000. What is the probability that you get a prize?
Discussion
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Source and history
- task_id
89901725-217d-5574-8738-f0166fafe25d- task_key
test--89901725-217d-5574-8738-f0166fafe25d- task_revision_id
- 1
- config / split
- / test
initial import