How Probabilities Are Determined
Section 7-1
| Activity Name | Activity Description |
|---|---|
| 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. |
| Crazy Choices Game | Students represent simple chance games as theoretical probabilities by entering data on 'winning' and total outcomes. Students can then simulate a number of trial runs to generate experimental data and probabilities for comparison with theoretical values. |
| 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. |
| Dice Table | Students input a set of 'winning' conditions for multiple players in a dice rolling game. The applet charts the possible outcomes on a two dimensional chart. Students then determine the probability of winning for a given player as a ratio, reduced fraction, converted decimal and percent chance. |
| 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. |
| 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. |
