Module 5: Introduction to Probability This module roughly corresponds to chapter 4 in the textbook. However, the textbook (both of them) unnecessarily makes this material much more complicated than it really is. This is probably the simplest module in the course. To help students improve their homework grade, There will be 5 homework problems associated with this module and it’s my hope everyone will score well on them, thus providing a boost to your overall homework grade. There are essentially two parts to this module: 1. Counting Rules 2. Probability The calculations are fairly simple and can easily done with a calculator or Excel. Your choice.
Module 5: Introduction to Probability Part 1: Counting Rules There are three counting rules we’ll cover: a. The “mn” counting rule. b. The sampling from a population with replacement counting rule. [Also called the “(N) n ” counting rule. c. The sampling from a population without replacement counting rule. What these rules have in common is that they are used to count possible outcomes. The best way to explain them is through examples.
Module 5: Introduction to Probability Part 1: Counting Rules a. The “mn” counting rule. Some call this the “refrigerator rule”. “mn” example 1: Suppose I want to buy a refrigerator. I go to Home Depot and select a particular model. The salesman tells me the model I’ve chosen: Comes in 4 sizes (small, medium, large, and extra large) Has 3 freezer positions (top, bottom, side) Comes in 7 colors (white, off-white, almond, stainless steel, black, metallic gray, and puke green) Comes with 3 interior rack configurations Has 2 types of controls (digital and dial) 2 delivery options (pickup and home delivery) Given this, how many possible outcomes can I choose from when making this purchase? 4 x 3 x 7 x 3 x 2 x 2 = 1008 possible outcomes.
Module 5: Introduction to Probability Part 1: Counting Rules “mn” example 2: Suppose I want to buy a 2016 Honda Accord. I go to Honda of Mentor and find that: There are 2 different door styles (2-door and 4-door) There are 9 different colors There are 4 different trim lines (EX, LX, EX-L, Touring) There are 2 different engines (4-cyl, 6 cyl) steel, black, metallic gray, and puke green) There are 2 different transmissions (manual and automatic) How many 2016 Honda Accords can I choose from? 2 x 9 x 4 x 2 x 2 = 288
Module 5: Introduction to Probability Part 1: Counting Rules b. The sampling from a population with replacement counting rule. This rule has a simple formula: (N) n Where N = Population Size; n = sample size The key here is that a single element in the population can be chosen more than once. In other words, it can be “replaced.” The most common applications of this rule are rolling dice and flipping coins. I can roll a die once and get a 6, I can roll it again and get another 6, and so on. I can flip a coin and get tails, then flip it again and get tails again.
Module 5: Introduction to Probability Part 1: Counting Rules Sampling from a population with replacement counting rule Example 1: Suppose I roll a die 4 times. How many possibilities are there in terms of possible outcomes?