exercise:B6af6f0f8c: Difference between revisions
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(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...") |
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<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>. | |||
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 00:11, 13 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].