Abstract
Before discussing probabilities, we discuss the kinds of events whose probabilities we want to consider, make their meaning precise, and study various operations with them.
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Notes
- 1.
Recall that the usual notation for a set is a list of its members between braces, with the members separated by commas. More about this in the next section.
- 2.
In the equation S = { S, H, D, C}, the S on the left denotes the sample space and the S on the right denotes “spade.” We did not want to change these convenient notations to avoid the conflict, since the meaning should be obvious.
- 3.
Recall that a set A is said to be a subset of a set B if every element of A is also an element of B.
- 4.
The face cards are J, Q, and K.
- 5.
Note that in Figure 2.3 the numerals designate the regions, but we prefer, somewhat against our conventions, to write braces and commas, e.g., {1, 4} instead of \(1 \cup 4\) and {1} instead of 1, in order to emphasize the use of these numerals as labels and not as numbers.
Fig. 2.3 
A general Venn diagram for three sets
- 6.
This proof is taken, with some modifications, from Alfred Rényi: Foundations of Probability, Holden-Day, San Francisco, 1970.
- 7.
In mathematics, we use “or” in the inclusive sense, that is, including tacitly the possibility “or both.”
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© 2016 Springer International Publishing Switzerland
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Schay, G. (2016). The Algebra of Events . In: Introduction to Probability with Statistical Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-30620-9_2
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DOI: https://doi.org/10.1007/978-3-319-30620-9_2
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