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math 2014
Shodor > SUCCEED > Workshops > Archive > math 2014

Today the class reviewed probability and looked at how probabilities serve as models. The students started by using M&Ms as a method of simulating population growth. The experiment began by pouring 5 M&Ms out of a cup and adding in as many additional M&Ms as those that land with the M side up and then repeating, which simulates exponential growth. Students then explored how averages of all their different values were similar to the theoretical values probability predicted. The students explored the Law of Large Numbers with a coin toss and examined true randomness. Then the students looked at a game called Monty Hall to learn about the probability of making choices once all but two options have been eliminated. It created an intriguing effect where changing the original choice actually caused the probability of choosing the correct answer to increase drastically. They then explored the dynamics of probability with many choices, finding that the Law of Large Numbers takes longer to come into effect the more choices there are to make. Next the students looked at the roll of a die and looked at how consecutive dice rolls compound the initial probability in a cumulative fashion. The class concluded by evaluating how rolling two dice changed the weight of different outcomes due to the combinations that can be made.