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Mathematics-Online problems:

Interactive Problem 1356: Yahtzee

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The object of the game ``Yahtzee'' is to make as advantageous scoring combinations as possible by rolling five dice. There are, among others,
\includegraphics[width=0.5\textwidth]{TdM_08_A3_bild1.eps}
\includegraphics[width=0.5\textwidth]{TdM_08_A3_bild2.eps}.

What is the probability of a Three-of-a-kind and a Small Straight, respectively, in the very first roll?


Let us assume that you obtained the combination

\includegraphics[clip, width=0.5\textwidth]{TdM_08_A3_bild3.eps},
which you would like to improve by another roll.


Determine the probability that you achieve Assume that in each case of re-rolling the best possible choice is made among the dice.


Answer:

Probability of
a Three-of-a-kind:
a Small Straight:
$ \left. \rule {0pt}{3.5ex} \right\}$ in one roll

Probability of
at least three identical faces:
at least four sequential faces:
$ \left. \rule {0pt}{3.5ex} \right\}$ when re-rolling

(The results should be correct to four decimal places.)


   

see also:

  automatically generated: 8/11/2017