Tutorial 1
MATH 215. Probability & Statistics.
Exercise 1. Given the universal set U cfw_1, 2,3, 4,5, 6, 7,8,9 and the sets A cfw_1, 2,5, 6 , B cfw_2,5,7 ,
and C cfw_1,3,5,7, 9 , find
1.
2.
A B and A C
A B and A C
3.
4.
5.
6.
A and C
A B and A C
A B and A
Conditional Probability
Conditional Probability:
The probability of occurring an event A when it is known
that some event B has occurred is called the conditional
probability of A given B and is denoted P(A|B).
P A B
P A | B
,
P B
P B 0
Notes:
P A B
1.
Probability of an Event
Definition of Terminology
Experiment: Procedure (or process) that we do and it
results in an outcome.
Sample Space (S): The set of all possible outcomes of a
experiment.
Event (E): The subset of a sample space, saying that
ES.
E
Counting Sample Points
Counting Example
Super Junior (n=10)
Girls Generation (n=9)
A fan will give a chocolate to either a member of
Super Junior or a Girls Generation. How many
different choices are there?
The Sum Rule
Example:
The department will award
Set Theory
Set Operation
Example of Sets
Girls Generation (n=9)
Super Junior (n=10)
SJ = cfw_LT, YS, KI, SD, SM, EH, DH, SW, RW, KH
GG=cfw_TY, J, S, T, HY, Y, SY, YA, SH
Set Theory
Set: Collection of objects (elements)
aA
a is an element of A
a is a m
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Tutorial 2
MATH 215. Probability & Statistics.
Exercise 1. A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students.
The final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received
Random Variable
Definition:
A Random Variable X is a function that associates each
element in the sample space with a real number.
HH
HT
TH
TT
Types of Random Variables:
A random variable X is called a discrete random variable
if its set of possible value