exercise:B6af6f0f8c: Difference between revisions

From Stochiki
(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> <math>2n</math> balls are chosen at random from a total of <math>2n</math> red balls and <math>2n</math> blue balls. Find a combinatorial expression for the probability that the chosen balls are equally divided in color. Use Stirling's formula t...")
 
No edit summary
 
Line 1: Line 1:
<div class="d-none"><math>
<math>2n</math> balls are chosen at random from a total of <math>2n</math> red balls and <math>2n</math> blue balls.  Find a combinatorial expression for the probability that the chosen balls are equally divided in color.  Use Stirling's formula to estimate this probability.  Using ''' BinomialProbabilities''', compare the exact value with Stirling's approximation for <math>n = 20</math>.
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}</math></div> <math>2n</math> balls are chosen at random from a total of <math>2n</math> red
balls and <math>2n</math> blue balls.  Find a combinatorial expression for the probability that
the chosen balls are equally divided in color.  Use Stirling's formula to estimate
this probability.  Using ''' BinomialProbabilities''', compare the exact value with Stirling's
approximation for <math>n = 20</math>.

Latest revision as of 23:11, 12 June 2024

[math]2n[/math] balls are chosen at random from a total of [math]2n[/math] red balls and [math]2n[/math] blue balls. Find a combinatorial expression for the probability that the chosen balls are equally divided in color. Use Stirling's formula to estimate this probability. Using BinomialProbabilities, compare the exact value with Stirling's approximation for [math]n = 20[/math].