Geburtstage, Wuerfel, Produkte und Karten

TL;DR

This paper explores elementary probability problems involving birthday coincidences, dice throws, card game combinatorics, and products of random numbers, providing novel examples for teaching introductory probability concepts.

Contribution

It presents new, original probability examples and problems suitable for elementary or introductory lectures, not previously documented in other sources.

Findings

Analysis of multiple birthday coincidences

Properties of products of uniform random numbers

Combinatorial insights into the card game Doppelkopf

Abstract

This article, based on a talk, treats some elementary, but not completely simple examples from probability. They concern multiple birthday coincidences, throwing dice, the combinatorics of the German card game "Doppelkopf", and the properties of products of uniformly distributed random numbers. The material, a lot of which was not taken from or found in other sources, should be of interest to all those who lecture or plan to lecture on probability, especially on an elementary or introductory level, and are looking for challenging examples or problems.