Emperical Probability
Section 9-1
| Activity Name | Activity Description |
|---|---|
| Spinner | Students can adjust the number of sectors on a game spinner drawn by the applet, and then compare theoretical probabilities, calculated from percentage of spinner area, against empirical 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 theoretical probabilities, calculated from percentage of spinner area, against empirical probabilities, calculated as a percentage of trial 'spins' initiated by the student. |
| 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. |
| 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 empirical data for discussion of conditional probability. |
| 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 empirical 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 empirical 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 empirical probabilities on the 'stay' or 'switch' choice given the number of doors in the particular game. |
| 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. |
