Settle Down Now!
Calvin Armstrong, Sifuna Bernard Mango, Avery Pickford, Karen Wilson*, Darryl Yong
Shall we shuffle... again?
Avery Pickford, *Allen Martin, Alan Bond, Peter Herreshoff
This activity explores what happens when a probabilistic game is played many times. These ideas are explored in two contexts: a frog jumping in a lily pond and a pizza delivery service. In essence, this activity gets students to explore the connection between transition probabilities of a Markov chain and its steady-state probability distribution without explicitly mentioning those terms or using linear algebra. No prior knowledge of Markov chains is required for the activity. It is suitable for students who have had minimal experience with probability.
This lesson plan constructs concepts of probability and randomness through explorations around various shuffling methods and dice rolling. It covers the concepts of permutations, expected value, equal likelihood, randomness, sample space, and wait time.
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.