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9/18/2008
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STAT 2000
Chapter 5
Probability
AgrestiFranklin
Terminology and Definitions
:
Tossing a coin would be considered a
random
phenomenon
because the outcome is uncertain.
It could be heads or it could be tails.
Probability
is a way of measuring this uncertainty
is a way of measuring this uncertainty.
If we toss a balanced coin 4 times, we are not
assured of getting exactly two heads and two tails.
But if we toss a balanced coin a large number of
times …
According to the
Law of Large Numbers
, if we
repeatedly toss a balanced coin, the proportion
of times a head will occur will get closer and
closer to 0.5.
We call this number the probability of getting a
head
head.
In repeated trials of a random phenomenon, the
proportion of times a certain outcome is
observed will approach a number that we call
the
probability
of that particular outcome.
It is not always possible to repeat a random
phenomenon a large number of times to
determine objective information.
Sometimes we have to rely on
subjective
probability.
For example:
If I drive to class today, what is the probability that
I will find a parking place quickly?
We also rely on probability properties and rules.
Terminology and Examples
A
sample space
is the set of all possible outcomes
of a random phenomenon.
(It is denoted S.)
Ex: Toss a coin. Sample Space is {H, T}
Ex: Toss a die.
Sample Space is {1, 2, 3, 4, 5, 6}
An
event
is a subset of the sample space.
Ex: Toss a die.
Let E be the event an even number
is observed.
E = {2, 4, 6}
For the event E, getting an even number of dots on
a die toss, P(E)
= P(2) + P(4) + P(6)
= 1/6
+ 1/6
+ 1/6 = 3/6
The probability of an event A is denoted P(A), and
is determined by adding the probabilities of the
individual outcomes in the event.
E = {2,4,6}
IF the individual outcomes are equally likely,
P(A) =
#
of outcomes in the event A
# of outcomes in the sample space
=
#
of outcomes favorable to A
total # of outcomes
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You try: Toss two balanced coins.
What is the sample space?
What is the probability of getting two heads?
What is the probability of getting exactly one head?
What is the probability of getting two of a kind?
Properties of Probabilities
The probability of any outcome in the sample space
is between 0 and 1.
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 Spring '08
 smith
 Probability

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