Chapter 2: Probability
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PROBABILITY
The Frequentist Notion of Probability
Consider a process that can be repeated over and over again (forever), independently and under
the same conditions.
Probability describes the
relative frequencies
at which all possible
outcomes of the process occur.
These outcome probabilities are on a scale of 0 (never occurs) to 1 (always occurs), and the sum
of all outcome probabilities must be 1.
Probability of an event
–
the probability of an event
A
is the sum of the probabilities of all
sample points in
A
.
We have the following propertes:
x
±
²
1
0
d
d
A
P
x
± ²
0
I
P
x
± ²
1
S
P
And, if
±
,
,
,
2
1
A
A
A
is a sequence of
mutually exclusive
events, then
±
²
±
²
±
²
±
²
²
²
³
³
³
³
³
3
2
1
3
2
1
A
P
A
P
A
P
A
A
A
P
If an experiment has
N
equally likely outcomes and exactly
n
of those outcomes correspond to
event
A
, then the probability of event
A
±
²
N
n
A
P
Example 1:
a)
What is the chance of rolling a 5 with a fair, six-sided die?
b)
What is the chance of drawing the queen of spades from a deck of 52 cards?
c)
What is the chance of drawing a queen?
d)
What is the chance of rolling an even number with a fair, six-sided die?
3
³
is

Chapter 2: Probability
25
Example 2:
(p. 50, example 2.24)
A die is loaded in such a way that an even number is twice as likely to occur as an odd number.
If
E
is the event that a number less than 4 occurs on a single toss of the die, find
P(E)
Example 3:
Two fair, six-sided
dice are rolled.
What is the chance of getting…
(a)
a total of 4 spots?
(b)
a total of 7 spots?
.

Chapter 2: Probability
Addition Rule

26