Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
1/18
Probability & Statistics
Basic Probability 2
TRAN Hoang Tung
NGUYEN Minh Huong
NGUYEN Mai Chung
University of Science and Technology of Hanoi (USTH)
September 10, 2019

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms
Notations
are very important!

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms
Notations
are very important!
Today

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms
Notations
are very important!
Today
Conditional probability, total probability theorem, Bayes’
rule

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms
Notations
are very important!
Today
Conditional probability, total probability theorem, Bayes’
rule
Independence, conditional independence

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
2/18
The Course So Far
What we have learnt?
Probability model: sample space, axioms
Notations
are very important!
Today
Conditional probability, total probability theorem, Bayes’
rule
Independence, conditional independence
Counting

Probability &
Statistics
Conditional
Probabili-
ties
Independence
Counting
3/18
1
Conditional Probabilities
Definition
Total Probability Theorem
Bayes’ Rule
2
Independence
Definition
Conditional Independence
3
Counting
Counting Principle
Combinations

Probability &
Statistics
Conditional
Probabili-
ties
Definition
Total
Probability
Theorem
Bayes’ Rule
Independence
Counting
4/18
1
Conditional Probabilities
Definition
Total Probability Theorem
Bayes’ Rule
2
Independence
3
Counting

Probability &
Statistics
Conditional
Probabili-
ties
Definition
Total
Probability
Theorem
Bayes’ Rule
Independence
Counting
5/18
Introduction
Consider 2 experiments:

Probability &
Statistics
Conditional
Probabili-
ties
Definition
Total
Probability
Theorem
Bayes’ Rule
Independence
Counting
5/18
Introduction
Consider 2 experiments:
Roll a fair 6-sided die
Sample space
Ω =
Probability
P
(1) =
P
(2) =

Probability &
Statistics
Conditional
Probabili-
ties
Definition
Total
Probability
Theorem
Bayes’ Rule
Independence
Counting
5/18
Introduction
Consider 2 experiments:
Roll a fair 6-sided die
Sample space
Ω =
{
1
,
2
,
3
,
4
,
5
,
6
}
Probability
P
(1) = 1
/
6
P
(2) = 1
/
6

Probability &
Statistics
Conditional
Probabili-
ties
Definition
Total
Probability
Theorem
Bayes’ Rule
Independence
Counting
5/18
Introduction
Consider 2 experiments:
Roll a fair 6-sided die
Sample space
Ω =
{
1
,
2
,
3
,
4
,
5
,
6
}

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