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Probability PART 6 The Basics Definition 1: An experiment is an occurrence with a result that is uncertain before the experiment takes place. Definition 2: The set of all possible outcomes is called the sample space for the experiment. Definition 3: Given a sample space S, an event E is a subset of S. The outcomes in E are called favorable outcomes. Definition 4: The complement of an event E is the set of outcomes not in E. Definition 5: The Law of Large Numbers states that in order for an empirical probability to be close to the value of the theoretical probability, you must conduct the experiment a large number of times. Probability Distributions The probability of every element in the sample space must be between 0 and 1, inclusive. 2. If we add the probabilities of every element in the sample space, we must get 1. 3. If you have an event E that is a subset of your sample space S, then we can add the probabilities of all possible results in E to get the probability of E itself. 1. Addition Principle When presented with n different alternatives, each with a certain number of outcomes, then you simply add the outcomes to arrive at the total number of alternatives. Example: Our family would like to go somewhere this weekend. There are 5 museums, 3 movie theaters, and 15 parks we could go to. If we are going only one place, we have 5 + 3 + 15 = 23 alternatives. Multiplication Principle When presented with a sequence of n choices, each with a certain number of outcomes, then you multiply the outcomes to arrive at the total number of choices. Example: While at Baskin-Robbins I am building my own ice cream treat. I first have to choose cone, waffle cone, waffle bowl, or regular bowl. I then choose the base flavor and finally choose the second flavor. There are 4x31x31=3844 choices for a 2-scoop ice cream treat. Tips and Hints When looking at license plates, you have a sequence of choices. These choices include ten numbers for the digits place and twenty-six letters for the alphabet characters.