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MMLU-Pro / 8329 / Extend Example 1.4-6 to an n-sided die. That is, suppose that a fair n-sided…

Problem

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

question

Extend Example 1.4-6 to an nn-sided die. That is, suppose that a fair nn-sided die is rolled nn independent times. A match occurs if side ii is observed on the ii th trial, i=1,2,…,ni=1,2, \ldots, n. Find the limit of this probability as nn increases without bound.
Plain-text mathematical notation (without MathML)
Extend Example 1.4-6 to an n-sided die. That is, suppose that a fair n-sided die is rolled n independent times. A match occurs if side i is observed on the i th trial, i=1,2,…,n. Find the limit of this probability as n increases without bound.
Original LaTeX notation
Extend Example 1.4-6 to an $n$-sided die. That is, suppose that a fair $n$-sided die is rolled $n$ independent times. A match occurs if side $i$ is observed on the $i$ th trial, $i=1,2, \ldots, n$. Find the limit of this probability as $n$ increases without bound.

category

math

options

  1. $1/\pi$
  2. $1 / e$
  3. $\pi/e$
  4. $e$
  5. $1-1/\sqrt{e}$
  6. $1/e^2$
  7. $1+1 / e$
  8. $ 1-1 / e$
  9. $1-(1/e^2)$
  10. $2/e$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8329
task_id
a920b166-4a73-5650-82f9-c41b80d8b77d
task_key
default--test--8329
task_revision_id
1
config / split
default / test

Official source

initial import