A Lesson in Probability and Statistics: Voyager/Scratch Coin Tossing Simulation

Submitted by Rich on Wed, 02/14/2018 - 19:25

This lesson introduces students to a variety of probability and statistics concepts using PocketLab Voyager and Scratch—ScratchX is not required.  The Scratch program simulates tossing any number of coins any number of times, displaying the number of heads in each toss with a square having varying shades of grey—black for zero heads and white for the maximum possible number of heads in each toss.  The simulated coins are tossed once each second with Voyager’s light sensor recording the results for each toss.

Activities for students include simulating the tossing of 4 coins 100 times.  Students become familiar with the concept of independence—the result from any toss is independent of all previous tosses of the coins.  From the light intensity data collected, students study randomness, the trend in running average, comparison of results with the binomial expansion coefficients in Pascal’s triangle, and runs in which the number of heads is the same for several successive tosses.  In an optional activity in which 256 coins are tossed 3000 times, students discover a distribution with a narrow central peak and near zero probabilities elsewhere.

For computer science students, the teacher can discuss the Scratch code and ask students how to modify the code so that dice are tossed instead of coins.  This can be used to introduce the concepts of probability of success, probability of failure, and mutually exclusive outcomes.

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Voyager/Scratch Coin Tossing Simulation
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