Probability basics
Typically found around Chapter 4 of an elementary statistics book.
Sources for this information are [JK10] and [Blu4].
[JK10 Chapter 4]
4.1 Motivational chapter example – M&Ms
4.2 Probability of Events – definition, notation,
tree diagrams, Venn diagrams, Empirical vs.
Theoretical probabilities, 0 ≤ 𝑃(𝐴) ≤ 1,
∑ 𝑃(𝐴) = 1, Law of Large Numbers, expressing
probabilities as odds for or against
4.3 Conditional Probability – given a table of
percentages, given a table of counts,
4.4 Rules of Probability – Complementary events,
the Complement Rule 𝑃(𝑛𝑜𝑡 𝐴) = 1 − 𝑃(𝐴),
The General Addition Rule:
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
The General Multiplication Rule:
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵|𝐴)
4.5 Mutually Exclusive Events, 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0
Special Addition Rule:
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 0
And its generalization to three or more events.
[Blu4 Chapter 4]
4.1 Introduction
4.2 Sample Spaces and Probability
Same, but omits Venn Diagram.
Explicit rules 𝑃(𝐴) = 0 for impossible event
And 𝑃(𝐴) = 1 for a certain event.
Brief discussions of “Subjective probability” and
“Probability and Risk-Taking”.
4.3 The Addition Rules for Probabilitiy.
Definition of Mutually Exclusive events
They present both
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
and 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 0
in this section, but not the multiplication rules.
4.4 The Multiplication Rules and Conditional
Probability. Definition of Independent Events.
They present both
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵) and
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵|𝐴) in this section.
And also 𝑃(𝐵|𝐴) =
𝑃(𝐴 𝑎𝑛𝑑 𝐵)
.
𝑃(𝐴)
4.6 Independent events and Dependent Events
Special Multiplication Rule
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
And its generalization to three or more events.
4.5 Counting Rules
𝑘1 ∙ 𝑘2 ∙ 𝑘3 ∙ ⋯ ∙ 𝑘𝑛
Definition of 𝑛!
Definition of 𝑛 𝑃𝑟 permutations
Definition of 𝑛 𝐶𝑟 permutations
4.7 Mutually Exclusive and Independence
Distinctions, differences, interactions
Not sure where the Probability and Counting Rules
are done.
4.6 Probability and Counting Rules
Not sure where the P(B|A) formula is introduced,
but they do use it suddenly in 4.7.
4.7 Summary