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.

As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…

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.

Discusses students' preconceptions of randomness and offers an alternative way to think about the concept using the idea of complexity. That is, the randomness of a sequence can be measured by the difficulty of encoding it. Methods of judging complexity and implications for teaching are discussed. (Contains 30 references.) (MKR)