The Hong Kong University of Science and Technology
MATH math 2421

Spring 2015
Chapter Two
2. Conditional Probability of an event
1
Conditional probability
So far, all (unconditional) probabilities were calculated with respect
to the sample space S.
However, in many situations, we can obtain some new information
such that we can upd
The Hong Kong University of Science and Technology
MATH math 2421

Spring 2015
Chapter Two
3. Law of total probability and
Bayes Theorem
1
Suppose that S is partitioned by a set of B1, B2, B3 and B4.
Exhaustive AND Mutually exclusive
A B4
A B1
B1
A
B4
B3
A B2
B2
S
A B3
A ( A B1 ) ( A B2 ) ( A B3 ) ( A B4 )
2
A ( A B1 ) ( A B2 ) ( A
The Hong Kong University of Science and Technology
MATH math 2421

Spring 2015
Chapter Two
1. Probability of an event
1
Probability
Originate from the study of games of chance and gambling during the 16th
century.
Be a measure of the possibility that a random phenomenon occurs, e.g.
the tossing of a dice.
Although we cannot exactl
The Hong Kong University of Science and Technology
MATH math 2421

Spring 2015
Math 2421 Probability
(Spring, 2015)
by
Dr. Yu, Chi Wai
1
Course Instructor: Dr. Yu, Chi Wai
Office: Room 3433
Email: [email protected]
Course webpage: http:/www.math.ust.hk/~macwyu/
Office Hours:
3:00pm 4:00pm (Mon)
or by appointment
2
MATH2421
Grading of th