Concept
What are outcomes and sample spaces?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Since life is uncertain, we don’t know for sure what is going to happen. But let’s start by assuming we know what things might happen. Something that might happen is called an outcome. You can think of this as the result of an experiment if you want to, although normally we won’t be talking about outcomes that we have explicitly manipulated and measured via scientific means. It’s more like we’re just curious how some particular happening is going to turn out, and we’ve identified the different ways it can turn out and called them outcomes. Now we’ve been using the symbol Ω to refer to “the domain of discourse” or “the universal set” or “all the stuff we’re talking about.” We’re going to give it yet another name now: the sample space. Ω, the sample space, is simply the set of all possible outcomes. Any particular outcome — call it O — is an element of this set, just like in chapter 1 every conceivable element was a member of the domain of discourse. If a woman is about to have a baby, we might define Ω as { boy, girl }. Any particular outcome o is either boy or girl (not both), but both outcomes are in the sample space, because both are possible. If we roll a die, we’d define Ω as { 1, 2, 3, 4, 5, 6 }. If we’re interested in motor vehicle safety, we might define Ω for a particular road trip as { safe, accident }. The outcomes don’t have to be equally likely, an important point we’ll return to soon."
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