exercise:524e66445a: 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> Gerolamo Cardano in his book, ''The Gambling Scholar,'' written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6---a different numb...") |
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Gerolamo Cardano in his book, ''The Gambling Scholar,'' written in the early 1500s, considers the following carnival game. There are six | |||
written in the early 1500s, considers the following carnival game. There are six | |||
dice. Each of the dice has five blank sides. The sixth side has a number between | dice. Each of the dice has five blank sides. The sixth side has a number between | ||
1 and 6---a different number on each die. The six dice are rolled and the player | 1 and 6---a different number on each die. The six dice are rolled and the player | ||
wins a prize depending on the total of the numbers which turn up. | wins a prize depending on the total of the numbers which turn up. | ||
<ul><li> Find, as Cardano did, the expected total without finding its distribution. | <ul style="list-style-type:lower-alpha"><li> Find, as Cardano did, the expected total without finding its distribution. | ||
</li> | </li> | ||
<li> Large prizes were given for large totals with a modest fee to play the game. | <li> Large prizes were given for large totals with a modest fee to play the game. | ||
Latest revision as of 16:32, 14 June 2024
Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6---a different number on each die. The six dice are rolled and the player wins a prize depending on the total of the numbers which turn up.
- Find, as Cardano did, the expected total without finding its distribution.
- Large prizes were given for large totals with a modest fee to play the game. Explain why this could be done.