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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


Source: Anderson, David F. - Department of Mathematics, University of Wisconsin at Madison


Collections: Mathematics