1.5 The Definition of Probability
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If A1, . . . , Ak are disjoint, Pr ki=1Ai = ki=1 Pr(Ai ).
Pr(Ac ) = 1 Pr(A).
A B implies that Pr(A) Pr(B).
Pr(A B) = Pr(A) + Pr(B) Pr(A B).
It does n
2.1 The Definition of Conditional Probability
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conditional on. For example, the multiplication rule for conditional probabilities becomes Pr(A1 A2 |B) = Pr(A1|B) Pr(A2 |A1 B). A partition is a colle
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Chapter 2 Conditional Probability
5. Suppose that on each play of a certain game, a person is
equally likely to win one dollar or lose one dollar. Suppose
also that the persons goal is to win two d
2.2 Independent Events
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Summary
A collection of events is independent if and only if learning that some of them occur
does not change the probabilities that any combination of the rest of them occur
2.3 Bayes Theorem
2. Consider again the conditions of Example 2.3.4 in this
section, in which an item was selected at random from
a batch of manufactured items and was found to be defective. For which
1.4 Set Theory
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Summary
We will use set theory for the mathematical model of events. Outcomes of an experiment are elements of some sample space S, and each event is a subset of S. Two
events both o
1.7 Counting Methods
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Summary
A simple sample space is a finite sample space S such that every outcome in S has the
same probability. If there are n outcomes in a simple sample space S, then each on
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Chapter 1 Introduction to Probability
It is shown in books on elementary calculus that the sum of the infinite series on
the right side of this equation is 1 (1/e), where e = 2.71828. . . . Hence,
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Chapter 1 Introduction to Probability
parts are. For example, for i = 2, it does not require that the same n2 possibilities
be available for x2 regardless of what x1 is. It only requires that the n
1.8 Combinatorial Methods
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examples in which more than one counting technique was required at different points
in the same problem. Sometimes, more than one technique is required to count the
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