Multistage Experiments with Tree Diagrams and Geometric Probabilities

Section 7-2

Activity Name Activity Description
Two Colors Applet The applet provides a conditional probability experiment whereby three boxes are pre-arranged to contain three possible combinations of colored marbles: two green, two red, and one red/one green. Students can run individual and multiple trials of drawing single marbles from a randomly chosen box. The applet accumulates trial results, providing experimental data for discussion of conditional probability.
Marbles Students input conditions representing a sequence of trials whereby colored marbles are randomly drawn from a bag. The applet accumulates data on the outcomes of each trial simulation, providing theoretical and experimental probabilities for direct comparison.
Spinner Students can adjust the number of sectors on a game spinner drawn by the applet, and then compare expected probabilities, calculated from percentage of spinner area, against experimental probabilities, calculated as a percentage of trial 'spins' initiated by the student.
Adjustable Spinner Students can adjust the number of sectors as well as the percentage covered by each sector to create a game spinner drawn by the applet. Students can then compare expected probabilities, calculated from percentage of spinner area, against experimental probabilities, calculated as a percentage of trial 'spins' initiated by the student.
Simple Monty Hall In the style of the TV program "Let's Make a Deal", students choose one of three doors, and then choose to 'stay' or 'switch' after a second door is revealed as a 'losing' choice. The applet compiles experimental probabilities on the value of the 'stay' or 'switch' choice.
Generalized Monty Hall Students select conditions for a series of "Let's Make a Deal" trials. The applet provides experimental data for 'number of wins' for a given set of trial simulations.
Advanced Monty Hall Students select conditions for a "Let's Make a Deal"-style game, and can play individual trials of the game. The applet compiles experimental probabilities on the 'stay' or 'switch' choice given the number of doors in the particular game.
Racing Game with One Die Students set conditions for a virtual auto race based on the rolling of a die. Students can then use the applet to observe individual races or to accumulate experimental probability statistics from multiple races. Discussion can focus on determination of complex probabilities using experimental observation.
Racing Game with Two Dice Students use an outcome table to set conditions for a virtual race based on the rolling of two dice. Students can then use the applet to observe individual races or to determine the results from a set of races. Discussion can focus on determination of complex probabilities using experimental observation.
Fire!! The applet provides a simulation of how a fire spreads through a stand of trees. Students input the probability, in decimal or fraction form, that a tree will catch fire given proximity to a burning tree. The applet graphically displays the burning of the forest and calculates a percentage destroyed . Discussion should focus on the relationship between multistage probability and chaos.
Directable Fire!! The applet provides a simulation of how a fire spreads through a stand of trees. Students can vary the size of the grid of trees, and can input a set of probabilities, in decimal or fraction form, that a tree will catch fire given proximity in a particular direction to a burning tree. The applet graphically displays the burning of the forest and calculates a percentage destroyed . Discussion should focus on the relationship between multistage probability and chaos.