Example: Fair Dice

(related to Definition: Laplace Experiments and Elementary Events)

A well-known example of a Laplace experiment is rolling a six-sided dice, for which each rolling a number \(\omega\in \{1,2,3,4,5,6\}\) has the probability of \(\frac 16\).

Die_Faces

For the event \(A\)="the number of rolled dots is even" we have then \(p(A)=\frac 36=\frac 12\), because there are \(3\) even numbers (favorable elementary events) in relation to \(6\) events in total.

For the event \(B\)="the number of rolled dots is smaller then 5" we have then \(p(B)=\frac 46=\frac 23\), because there are \(4\) numbers smaller then \(5\) (favorable elementary events) in relation to \(6\) events in total.


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References

Bibliography

  1. Bosch, Karl: "Elementare Einf├╝hrung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition