Popular game shows offer educators the opportunity to develop active-learning exercises that provide students with a real-world connection to analytical reasoning and methods. We describe a classroom assignment developed for quantitative business courses based on the Monty Hall Problem (MHP), a probability puzzle with ties to the long-running…

Describes the development and instructional use of a Microsoft Excel spreadsheet template that facilitates analytical and Monte Carlo risk analysis of investment decisions. Discusses a variety of risk assessment methods followed by applications of the analytical and Monte Carlo methods. Uses a case study to illustrate use of the spreadsheet tool…

Investigates the commonly suggested rounding rule for addition and subtraction including its derivation from a basic assumption. Uses Monte-Carlo simulations to show that this rule predicts the minimum number of significant digits needed to preserve precision 100% of the time. (Author/KHR)

Investigates the standard rounding rule for multiplication and division including its derivation from a basic assumption. Uses Monte-Carlo simulations to show that this rule predicts the minimum number of significant digits needed to preserve precision only 46.4% of the time and leads to a loss in precision 53.5% of time. Suggests an alternative…

Presents a Monte Carlo simulation on probability using a telephone directory as a pseudorandom-number generator. Claims that Monte Carlo simulations offer a way to teach probability concretely and with understanding and that students enjoy the probability experiments. (ASK)

Describes an activity designed to demonstrate the birthday paradox and introduce students to real-world applications of Monte Carlo-type simulation techniques. Includes a sample TI-83 program and graphical analysis of the birthday problem function. (KHR)

Investigates the cereal box problem using both an experimental and theoretical framework, and Monte Carlo methods. Using empirical data, students can discover patterns and relationships that help them understand the origin of the theoretical solution to the problem. Contains 17 references. (Author/ASK)

Creates graphs to see how the relative frequency of an event tends to approach the probability of that event as the number of trials increases. Uses a simulation of a poker machine to provide context for this subject. (ASK)

The uses of random number generators are illustrated in three ways: (1) the solution of a probability problem using a coin; (2) the solution of a system of simultaneous linear equations using a die; and (3) the approximation of pi using darts. (MP)

Demonstrated is the use of BASIC computer programs to simulate a binomial experiment and test a simple statistical hypothesis. The theoretical results are reached with the third programing attempt. All results, as well as computer programs, are included. (JJK)

Monte Carlo methods are used to simulate activities in baseball such as a team's "hot streak" and a hitter's "batting slump." Student participation in such simulations is viewed as a useful method of giving pupils a better understanding of the probability concepts involved. (MP)

Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)

Some activities designed around the Monte Carlo method of solving probability problems are described. The instructional applications of this method involve physical models or simple BASIC computer programs. (MP)

The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing random sampling simulations with a computer. Presents a program written in Quick BASIC simulating the steps of the Monte Carlo method. (ASK)

The Monte Carlo procedure of generating random points that lie within the unit square is used to approximate pi, as the ratio of points within the first quadrant of the unit circle to the total number of randomly generated points. A BASIC computer program for this method is included. (JJK)