STAT 509  Section 3.1:
Probability
Basic Definitions
Sample Space
(of an experiment):
The collection of all
the possible outcomes (or sample points).
Example 1.
Record plant location (either 1, 2, 3) of next
maintenance call for spinning machine repair:
Sample space =
Example 2.
Toss 2 fair coins:
Sample space =
Example 3.
An engineering design firm is up for a
Nissan contract and a Ford contract:
Sample space =
The probability
of a sample point is a number between
0 and 1 that measures the likelihood that this outcome
will occur when the experiment is performed.
Often we take this to mean the proportion of times the
outcome would occur if we repeated the experiment
many times.
Note:
(1)
All sample point probabilities must be between 0
and 1.
(2)
The probabilities of all the points in the sample
space must sum to 1.
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Example 1:
Plant 1 has 22 machines, plant 2 has 60
machines, plant 3 has 18 machines.
Probability of next
repair being from plant 3, denoted:
P(3) =
Assumption?
An event
is an outcome or collection of outcomes.
We typically determine the probability of an event by
adding the probabilities of the distinct outcomes that
make up the event.
Example 1:
Event A = ‘next repair from oddnumbered
plant’
P(A) =
Example 3:
Event B = ‘get at least one contract’
P(B) =
Unions and Intersections
Compound events
are composed of two or more “simple
events,” for example:
The union
of events A and B is the event that either
A or
B (or both) occurs.
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 Fall '08
 CHALMERS
 Probability, Probability theory, useful life, software problem

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