Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

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)

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

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)

Three computer programs are listed for finding binomial probabilities. Other applications and variations are 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 subject matter presented in this article can be used in the classroom to enrich the learning experience of students taking a course that includes a unit on combinatorics, such as discrete mathematics, graph theory, or probability. In order to provide such students with the background needed to appreciate the significance of the generalization…

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)

"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,…