# Two_textbooks

```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&amp;Ms
4.2 Probability of Events – definition, notation,
tree diagrams, Venn diagrams, Empirical vs.
Theoretical probabilities, 0 ≤ π(π΄) ≤ 1,
∑ π(π΄) = 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 π(πππ‘ π΄) = 1 − π(π΄),
π(π΄ ππ π΅) = π(π΄) + π(π΅) − π(π΄ πππ π΅)
The General Multiplication Rule:
π(π΄ πππ π΅) = π(π΄) β π(π΅|π΄)
4.5 Mutually Exclusive Events, π(π΄ πππ π΅) = 0
π(π΄ ππ π΅) = π(π΄) + π(π΅) − 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 π(π΄) = 0 for impossible event
And π(π΄) = 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
π(π΄ ππ π΅) = π(π΄) + π(π΅) − π(π΄ πππ π΅)
and π(π΄ ππ π΅) = π(π΄) + π(π΅) − 0
in this section, but not the multiplication rules.
4.4 The Multiplication Rules and Conditional
Probability. Definition of Independent Events.
They present both
π(π΄ πππ π΅) = π(π΄) β π(π΅) and
π(π΄ πππ π΅) = π(π΄) β π(π΅|π΄) in this section.
And also π(π΅|π΄) =
π(π΄ πππ π΅)
.
π(π΄)
4.6 Independent events and Dependent Events
Special Multiplication Rule
π(π΄ πππ π΅) = π(π΄) β π(π΅)
And its generalization to three or more events.
4.5 Counting Rules
π1 β π2 β π3 β β― β ππ
Definition of π!
Definition of π ππ permutations
Definition of π πΆπ 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
```