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MMLU-Pro / 7886 / An urn contains four balls numbered 1 through 4 . The balls are selected one at…

Problem

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

question

An urn contains four balls numbered 1 through 4 . The balls are selected one at a time without replacement. A match occurs if the ball numbered mm is the mm th ball selected. Let the event AiA_i denote a match on the ii th draw, i=1,2,3,4i=1,2,3,4. Extend this exercise so that there are nn balls in the urn. What is the limit of this probability as nn increases without bound?
Plain-text mathematical notation (without MathML)
An urn contains four balls numbered 1 through 4 . The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the m th ball selected. Let the event A_(i) denote a match on the i th draw, i=1,2,3,4. Extend this exercise so that there are n balls in the urn. What is the limit of this probability as n increases without bound?
Original LaTeX notation
An urn contains four balls numbered 1 through 4 . The balls are selected one at a time without replacement. A match occurs if the ball numbered $m$ is the $m$ th ball selected. Let the event $A_i$ denote a match on the $i$ th draw, $i=1,2,3,4$. Extend this exercise so that there are $n$ balls in the urn. What is the limit of this probability as $n$ increases without bound?

category

math

options

  1. $1 - \frac{1}{e}$
  2. $\frac{1}{e}$
  3. $\frac{1}{n!}$
  4. $\frac{1}{\sqrt{n}}$
  5. $\frac{1}{4}$
  6. $\frac{2}{e}$
  7. $\frac{1}{2}$
  8. $e^{-1/n}$
  9. $\frac{n-1}{n}$
  10. $\frac{1}{n}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
7886
task_id
a16778d8-c424-5463-933d-a9f235845e25
task_key
default--test--7886
task_revision_id
1
config / split
default / test

Official source

initial import