Assignment 2

About the Activity

This activity explores how probability can be used to make decisions in the board game Catan. In the game, players roll two dice, and settlements produce resources when the sum of the dice matches the number of an adjacent hexagon.

Participants compare two possible settlement locations and investigate which one is more likely to produce resources. They first calculate theoretical probabilities using the sample space of two dice.

They then use an online probability simulation to generate experimental results and compare them with their theoretical predictions.

The activity encourages participants to distinguish between expected outcomes and guaranteed results, particularly when the number of dice rolls is small.

Learning Objectives

By the end of this activity, participants should be able to:

1. Determine theoretical probabilities for the sums of two fair dice.
2. Calculate the probability that a particular settlement will produce a resource.
3. Use an online simulation to collect experimental data.
4. Compare theoretical probabilities with experimental production rates.
5. Explain why a higher expected resource production does not guarantee a better outcome in every short sequence.

Interactive Probability Applet

The activity uses the AZRS Probability Lab to simulate repeated rolls of two fair dice.

Select the Two Dice (Sum) option to investigate the distribution of dice sums.

Participants use the simulation to record experimental frequencies and compare the production rates of the two settlements.

Open Probability Applet

Activity Documents

The following documents contain the detailed activity plan and the student worksheet.