Permutations & Combinations -Course Description
Monday, August 13, 2012
In this course, we explore the world of probability theory. This course constitutes a basic introduction to the theories behind modern statistics. We begin by studying permutations of independent events, and apply the Fundamental Counting Principle. For example, how many four-character passwords are possible given upper case letters, lower case letters, and digits 0-9? Then we move to permutations “without replacement” (dependent events), and learn about factorial (!) as a mathematical operation. An example problem here might be: How many baseball lineups can I make with 9 players? Then, we move to combinations, where order does not matter. For example, how many ways can I choose five balls from a bag of ten? At this point, we have the tools to start asking basic probability questions involving coins, dice and cards. For instance: What is the probability of getting a six on one roll of a fair die? What is the probability of getting at least one six on two rolls of a fair die? What is the probability of getting a straight flush in a game of poker, using a well-shuffled standard deck? We perform empirical trials where we find the answers to our questions through flipping coins and rolling dice, and we gain a feel for Bernoulli's Principle that the experimental outcome approaches the theoretically calculated outcome more closely as more trials are performed. All of these ideas are connected to modern methods of commerce, including insurance and the state lottery. The goal is to give the student “statistical literacy,” an essential skill for the modern human being.
Faculty: Robert Wilson, High School Math Teacher
Class Dates: March 25th-April 26th, 2013
Curriculum Area: Morning Lesson Block
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