ISyE 2027 Probability with Applications
Polly B. He
Fall10, Week 1
What’s to be covered:
•
Administrative Notes
•
Chapter 2: Sample space, Events, Probability
•
Sets and Operations on them
•
Counting
What is this course about?
Think about things that are random and those that are not. Which one can you name
more?
Language to describe random experiments
Sample spaces
are sets whose elements describe the outcomes of the experiment in which we
are interested.
Example 2.1(a) Two possible outcomes from a single coin toss (if ignoring the possibility
that the coin lands on the edge): Ω =
{
H, T
}
.
Example 2.1(b) The month in which the birthday of the next person you meet on the street
falls: Ω =
{
Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec
}
.
Events
are subsets of the sample space. We say that an event
A
occurs if the outcome of the
experiment is an element of the set
A
.
Example 2.2(a) In the experiment of Example 2.1(a), we can ask for the outcomes that
correspond to a long month (with 31 days):
L
=
{
Jan, Mar, May, Jul, Aug, Oct, Dec
}
.
Example 2.2(b) As in the previous example, we may ask for the outcomes that correspond
to months that have the letter r in their (full) name:
R
=
{
Jan, Mar, Oct, Dec
}
.
Intersection
of sets
Example 2.2(c) If both
L
and
R
occur, the set
L
∩
R
is called the intersection of
L
and
R
.
L
∩
R
=
1
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of sets
Example 2.2(d) If at least one of the events
A
and
B
occurs, we have the union
A
∪
B
of
the two sets
A
and
B
.
L
∪
R
=
Complement
of
A
: if and only if
A
does
not
occur.
A
c
=
{
ω
∈
Ω :
ω /
∈
A
}
.
For example,
L
c
=
The
empty set
is the complement of Ω, denoted as
∅
.
If events
A
and
B
have no outcomes in common, i.e.,
A
∩
B
=
∅
, then
A
and
B
are
disjoint
or
mutually exclusive
.
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 Fall '08
 Zahrn
 Probability theory, Coin flipping, Bernoulli trial

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