Chapter 2 lecture notes Math 431, Spring 2011 Summary: Chapter 2 lecture notes Math 431, Spring 2011 Instructor: David F. Anderson Chapter 2: Axioms of Probability Section 2.2: Sample Space and Events We consider an experiment whose outcome is not predictable with certainty. However, we suppose that the set of all possible outcomes is known. Definition 1. The set of all possible outcomes of an experiment is the sample space of an experiment, and is denoted by S. Subsets of S are called events. Elements of S, x S, are called outcomes. · In this course, we will care about the probability of both events and specific outcomes. That is, P(E) and P({x}) = P(x). Example 1. A coin is tossed twice and the outcome of each is recorded. Then, S = {(H, H), (H, T), (T, H), (T, T)}. The event that the second toss was a Head is the subset E = {(H, H), (T, H)}. Example 2. Consider 3 light-bulbs. Our experiment consists of finding out which light-bulb burns out first, and how long (in hours) it takes for this to happen. S = {(i, t) : i {1, 2, 3}, t 0}, i tells you which one burns out, and t gives how long it lasted, in hours. The event that the Collections: Mathematics