exercise:9e83c3ee89: 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> 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...") |
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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:F4bf733f21|Exercise]]. Do you agree with him?) | |||
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 | |||
Do you agree with him?) | |||
Latest revision as of 20:09, 12 June 2024
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. Do you agree with him?)