# 1. Basic Probability Concepts

**Def 1.1:** The sample space is the set

**Questions…**

- What exactly does this mean?
- How is this different from ? The “1-1 correspondence” part makes me think that , where corresponds with the term “element” used in Def 1.1.

**Ex:** Experiment=tossing 3 fair coins

I think this corresponds with my , at least in the way that I’m thinking about . Perhaps the difference is that I’m thinking that there is only one way to represent the set of all outcomes when, in fact, it could be represented in multiple ways.

**Ex:**

, where corresponds with , corresponds with , etc. So all of these are “equivalent” representations of .

If that is the case, then I think that the definition of should be modified.

**Def 1.1′:** A sample space of an experiment is a set or .

**Comments…**

- I added the phrase “an experiment” to specify that a sample space corresponds with a particular experiment”.
- I changed “the sample space/set” to “a sample space/set” since there could be multiple representations

**Questions…**

- I wonder if my incorporation of representation is problematic. For example, does my definition now imply that , or does it allow for isomorphisms? Is there any value to viewing them as different? Or should ?How are these different? How are they the same?

I just looked up the definition of sample space in *A First Course in Probability* (Ross, 2006), and this is what I found:

“This set of all possible outcomes of an experiment is known as the sample space of the experiment and is denoted by ” (p. 24).

This definition corresponds with my .

**Citation**

Ross, S. (2006). *A First Course in Probability*. (7th ed.) Pearson Education: Upper Saddle River, NJ.