In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

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

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)

Investigates the problem of finding the expected number of questions necessary to identify 1 out of a set of 30 attribute blocks. Solutions include the use of a tree diagram or a computer simulation. Generalizes the problem for increased numbers of attributes. (MDH)

Describes a simulation-oriented computer microworld named CHANCE used to overcome the limitations of physical materials for experiments in teaching and learning introductory probability. Results of a teaching experiment conducted with four middle school and high school students are discussed. (15 references) (LZ)

Explains a proposed block of instruction that would give students in industrial engineering, operations research, systems engineering, and applied mathematics the basic understanding required to begin more advanced courses in simulation theory or applications. (DDR)

The purpose of this teaching unit is to approach elementary probability problems in three ways. First, actual trials are performed and results are recorded. Second, a simple computer simulation of the problem provided on diskette and written for Apple IIe and IIc computers, is run several times. Finally, the mathematical solution of the problem is…

Discussed are the use of probability simulations in a mathematics classroom. Computer simulations using regular dice and special dice are described. Sample programs used to generate 100 rolls of a pair of dice in BASIC and Logo languages are provided. (YP)

Discussed are solutions to the problem "What is the expected number of rolls for the total first to exceed 6?" Several algebraic solutions are presented. A computer program which may be used to simulate this problem is included. (CW)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

Presented is an activity in which probability and percents are taught using a basketball computer simulation. Computer programs that replicate the free-throw accuracy of college and professional stars and allow students to compete with those stars are included. (KR)

Some specific uses of microcomputers in mathematics instruction are presented. Included are examples for generating data and patterns, checking, practice of various types, developing understanding, comparing results, simulation of experiments, introducing new ideas, solving problems, and extending into new areas. Brief computer programs are given.…

These materials on geometric probability are the first unit in a course being developed by the Mathematics Department at the North Carolina School of Science and Mathematics. This course is designed to prepare high school students who have completed Algebra 2 for the variety of math courses they will encounter in college. Assuming only a knowledge…

"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,…