exercise:7b7fd6faf6: 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> You are presented with four different dice. The first one has two sides marked 0 and four sides marked 4. The second one has a 3 on every side. The third one has a 2 on four sides and a 6 on two sides, and the fourth one has a 1 on three sides...") |
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You are presented with four different dice. The first one has two sides marked 0 and four sides marked 4. The second one has a 3 on every side. | |||
two sides marked 0 and four sides marked 4. The second one has a 3 on every side. | |||
The third one has a 2 on four sides and a 6 on two sides, and the fourth one has a 1 | The third one has a 2 on four sides and a 6 on two sides, and the fourth one has a 1 | ||
on three sides and a 5 on three sides. You allow your friend to pick any of the four | on three sides and a 5 on three sides. You allow your friend to pick any of the four | ||
Latest revision as of 00:22, 14 June 2024
You are presented with four different dice. The first one has two sides marked 0 and four sides marked 4. The second one has a 3 on every side. The third one has a 2 on four sides and a 6 on two sides, and the fourth one has a 1 on three sides and a 5 on three sides. You allow your friend to pick any of the four dice he wishes. Then you pick one of the remaining three and you each roll your die. The person with the largest number showing wins a dollar. Show that you can choose your die so that you have probability 2/3 of winning no matter which die your friend picks. (See Tenney and Foster.[Notes 1])
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