STAT 515  Chapter 3:
Probability
Basic Definitions
Experiment
:
A process which leads to a single outcome
(called a sample point) that cannot be predicted with
certainty.
Sample Space
(of an experiment):
The collection of all
the possible outcomes (or sample points).
Example 1.
Roll 1 die:
Sample space =
Example 2.
Toss 2 coins:
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:
Probability of rolling a 3, denoted:
P(3) =
Example 2:
Assuming coin is fair, P(HH) =
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 = ‘rolling an even number’
P(A) =
Example 2:
Event B = ‘get at least one head’
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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 Spring '11
 Wright
 Accounting, Probability, Probability theory

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