Geburtstage, Wuerfel, Produkte und Karten

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.