9/18/2008
1
STAT 2000
Chapter 5
P
b bilit
Probability
Agresti-Franklin
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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