(for lazy ants who prefer to go down more often then up)
I really like this activity and took it one step further by finding the theoretical probability with counter devices.

After completing the Ants and the Aardvark activity, students will have an informal understanding that the sample space for the problem is not uniform. This activity will illustrate the theoretical probability for each of the outcomes by comparing the Join plot with the Combinations plot.

The sampler shown below uses a set of five inline counter devices to direct an ant through each of the decision points in the maze. The counter devices guarantee that each possible path is followed exactly one time, if the run value is correct. I used "a" and "b" instead of U for up and D for down because these are the default labels in TinkerPlots.

Task 1. Determine how many outcomes are necessary to follow each possible path. Run the sampler and create a plot with the join value on the horizontal axis. The Join plots indicate that there are 32 unique paths. In the plot on the right, the five outcomes that will result at hole 1 are grouped at the top.

You should notice that there are exactly five paths that lead to hole 1. You might recall that this could be found by noticing that there was only one "a" in the sequence of five letters. By now you might have noticed that sorting outcomes for the set of the holes is going to get complicated, even if they are color coded.
Letâ€™s use the Combination attribute in the Sampler Options to complete this action. The graphics below indicates this option. Pull down a new plot from the tool shelf and graph Combinations. Is this what you expected?

The Combinations attribute alphabetically sorts the items in the Join attribute, so order does not matter. Updated: June 2016

## Ants and Aardvarks

BACK TO PROBABILITY PAGEI really like this activity and took it one step further by finding the theoretical probability with counter devices.

After completing the Ants and the Aardvark activity, students will have an informal understanding that the sample space for the problem is not uniform. This activity will illustrate the theoretical probability for each of the outcomes by comparing the Join plot with the Combinations plot.

The sampler shown below uses a set of five inline counter devices to direct an ant through each of the decision points in the maze. The counter devices guarantee that each possible path is followed exactly one time, if the run value is correct. I used "a" and "b" instead of U for up and D for down because these are the default labels in TinkerPlots.

Task 1. Determine how many outcomes are necessary to follow

each possible path. Run the sampler and create a plot with the join value on the horizontal axis. The Join plots indicate that there are 32 unique paths. In the plot on the right, the five outcomes that will result at hole 1 are grouped at the top.You should notice that there are exactly five paths that lead to hole 1. You might recall that this could be found by noticing that there was only one "a" in the sequence of five letters. By now you might have noticed that sorting outcomes for the set of the holes is going to get complicated, even if they are color coded.

Letâ€™s use the Combination attribute in the Sampler Options to complete this action. The graphics below indicates this option. Pull down a new plot from the tool shelf and graph Combinations. Is this what you expected?

The Combinations attribute alphabetically sorts the items in the Join attribute, so order does not matter.

Updated: June 2016