The article asks about the minimal number of persons required for achieving a probability 1/2 that (a.) At least two share a birthday, (b.) At least one shares the reader's birthday. A basic question about the necessary number of checks underlies both problems.

The article presents an attempt to analyse Monty's dilemma by means of conversational formula-free dialogues and to simulate the problem by composing isomorphic stories. The crucial roles of specifying the underlying scenarios and explicating epistemic and probabilistic assumptions are highlighted.

Each weighted mean of two values has a counterpart, equidistant from the arithmetic mean, obtained by exchanging roles between the weights or by inversing each weight. These elementary relations are apt for introductory courses.

Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.

When two sealed envelopes contain money, one twice as much as the other, a player should be indifferent between them. But when one envelope is opened, one's decision should vary as a function of the observed value and one's subjective probabilities.

The older one gets, the more one's life expectancy exceeds the population's given expectancy (at birth). Yet longevity is finite. This apparent paradox is analysed probabilistically with reference to empirical demographic data.

An elusive probability paradox is analysed. The fallacy is traced back to improper use of a symbol that denotes at the same time a random variable and two different values that it may assume.

A coefficient of unfairness in the allocation of goods to people can be extended to measuring consensus among judges. The notion of relative variability underlies the formation of these measures.

The self-weighted mean ("WS')--in which each value is weighted by itself--is presented in several contexts and illustrated. It is incorporated in a set of more familiar means. Intuitions concerning "WS" are explored.