1
Dr. Maddah
ENMG 500
Eng’g Management I
01/18/09
Probability Primer
1
•
Sample space and Events
¾
Suppose that an experiment with an uncertain outcome is
performed (e.g., rolling a die).
¾
While the outcome of the experiment is not known in
advance, the set of all possible outcomes is known. This set is
the sample space,
Ω
.
¾
For example, when rolling a die
Ω
= {1, 2, 3, 4, 5, 6}. When
tossing a coin,
Ω
= {H, T}.
When measuring life time of a
machine (years),
Ω
= {1, 2, 3, …}.
¾
A subset
E
⊂
Ω
is known as an event.
¾
For example, when rolling a die,
E
= {1} is the event that one
appears.
The subset
E
= {1, 3, 5} is the event that an odd
number appears.
•
Probability of an event
¾
If an experiment is repeated for a number of times which is
large enough, the fraction of time that event
E
occurs is the
probability that event
E
occurs,
P
{
E
}.
¾
E.g., when rolling a fair die,
P
{1} = 1/6, and
P
{1, 3, 5} =
3/6 = 1/2.
When tossing a fair coin,
P
{H} =
P
{T} = 1/2.
1
Compiled from S. M. Ross,
Introduction to Probability Models
, 6
th
Edition, Academic Press, 1997.