Presents several theoretical solutions to a geometry problem involving circles and probability. Includes simulation procedures to estimate the solutions. (MKR)

Advantages and disadvantages of common ways to justify the answer to a probability problem are discussed. One explanation appears superior to the others because it is easy to understand, mathematically rigorous, generalizes to a broader class of problems, and avoids the deficiencies of the other explanations. (MNS)

Determines the theoretical probability that a regular polygon will cross a crack when dropped onto floorboards. By following two special cases, a pattern emerges that enables students to consider the general case. (ASK)

Explains a non-standard definition of an ellipse familiar to astronomers and workers in celestial mechanics but which is not usually given in undergraduate text books on mathematics. (MM)

One way in which a computer simulation can convince students of the validity of formulas for the density and distributive functions of the sum of two variables is described. Four computer program listings are included. (MNS)

An exercise simulating the tossing of N dice is described. Calculation of expected gain and extension to a two-person game are each discussed. (MNS)

Presents a problem that has been well received by students in undergraduate mathematical statistics courses. The problem is presented as a game in which students are asked to choose between two alternatives, as if they were betting. (ASK)

The game of craps is analyzed in terms of mathematical expectation. Betting examples are presented and discussed, and a computer simulation program in BASIC is included. (MNS)

Presents the game of Keno as an interesting, realistic model for applying mathematics that can be an excellent aid in teaching some basic probability concepts. It is felt that having students examine the probabilities may convince them that winning at Keno is unlikely, and it is an unfair game. (MP)

The widespread interest in sports in our culture provides an excellent opportunity to catch students' attention in mathematics and statistics classes. One mathematically interesting aspect of volleyball, which can be used to motivate students, is the scoring system. (MM)

How a computer randomly generates numbers to turn off lighted blocks on a graphics display is discussed. A computer program is given after reviewing a definition and two theorems and applying them to the problem. (MNS)

Presents noncalculus approximation techniques for two normal distribution problems. These methods may be useful projects for lower-level undergraduate statistics and computer science students. (PK)

Describes a five-dice game, horse. Discusses the offensive player's strategy using the ideas of probability, such as counting outcomes, mutually exclusive events, conditional probabilities, zero sum games, and the use of computer. (YP)

Explains a new way of viewing Bayes' formula. Discusses the revision factor and its interpretation. (YP)

"Gedankensimulation" is a term adapted from Einstein's "thought experiments" to indicate mentally created simulations that can help conceptualize ideas. Presents seven examples of simulations that can be utilized to solve problems or illustrate concepts in probability and statistics. Problem contexts include games of chance,…