Download Random Basic.nlogo (28 KB)
Random Basic is one of several interactive models for probability and statistics authored in the NetLogo modeling-and-simulation environment. The model is part of ProbLab, a curricular unit designed to enrich student understanding of the domain. The online unit package will include a suite of models, student worksheets, and a teacher guide. Below is an applet of Random Basic. You can interact with this model by changing the slider values and switch setting and then pressing Setup and Go to run this model under different settings. You may want to slow down the model in order to get to know it -- use the ADJUST SPEED slider that is on the top-left corner of the graphics window. For more details, please see the model itself in the NetLogo library or download the model here.
CM ProbLab: Random Basic -- Supporting an Exploration of Randomness
Don't see nothin'?
Random Basic was designed to focus learners on randomness, an issue that is naturally central to all ProbLab models. The basic sample space in 9-Block Stalagmite and 9-Blocks is just 2 -- green or blue are the only possible values for the property 'color,' in those models. So in those models the samples are made up either of green or blue events, and the sample space is "inflated" by considering compound events, such as blocks of 9 independent squares. In Random Basic, however, the space is generically larger. You may choose to work with a sample size of 2 by setting the SAMPLE SPACE slider to '2,' but you can also work in larger spaces (up to 100 in this version of the model).
Run the model and watch the creature deposit single square-events that are either green or red. Can you anticipate which column will hit the top first? Because the creature is building the columns one square at a time, there is absolutely no way we can predict which column will win when. The larger the sample space, the lower is our chance of guessing which column will win. It's totally, well, random. Or at least, pseudo-random. But we can make statements of a different nature: we can see trends in how, in general, the settings and the outcomes relate as we change the settings.
Questions to Ponder
Gap: As the experiment runs, does the 'gap' between the tallest and shortest column change (see the BIGGEST-GAP monitor)? Should it? When we make the yellow area taller and/or wider (by setting greater values for HEIGHT and SAMPLE-SPACE), does the 'gap' behave differently
%-RED: As the experiment runs, will the %-RED monitor be closer to the RED-GREEN slider setting? Further from it? The same? (This makes more sense for even and not odd RED-GREEN settings.) What happens for greater collections of outcomes, as when we have more HEIGHT and/or more SAMPLE SPACE? What happens for smaller value settings of the red-green slider?
Trials: How many trials does it take until the experiment stops running? For instance, set the sample-space to 100 and the HEIGHT to 2. Press GO. The moment one of the columns is 2 squares tall, it will stop the experiment. Look at the TOTAL-TRIALS monitor.
Change your mind?: Setup the model. Guess which column will fill up before other columns. Now run the model until some columns are taller than others. Stop the model. Will you change your guess now, based on what you see? Should you always guess that the tallest column will eventually win? Does that make sense? But anything can still happen, no?.. yes?..
%-FULL: A very difficult challenge is to determine the relation between %-FULL -- how much of the yellow rectangle is occupied by squares -- and the SAMPLE-SPACE and HEIGHT settings. Here is one thought.
[last updated July 8, 2005]