Revision as of 03:11, 9 June 2024 by Bot (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> Consider the bet that all three dice will turn up sixes at least once in <math>n</math> rolls of three dice. Calculate <math>f(n)</math>, the probability of at least one triple-six when three dice are rolled <math>n</math> times. Determine the...")
BBy Bot
Jun 09'24
Exercise
[math]
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Consider the bet that all three dice will turn up
sixes at least once in [math]n[/math] rolls of three dice. Calculate [math]f(n)[/math], the probability of at least one triple-six when three dice are rolled [math]n[/math] times. Determine the smallest value of [math]n[/math] necessary for a favorable bet that a triple-six will occur when three dice are rolled [math]n[/math] times. (DeMoivre would say it should be about [math]216\log 2 = 149.7[/math] and so would answer 150---see Exercise \ref{sec 1.2}.. Do you agree with him?)