4.1
Experiment:
When a process that results in one and only one of many observations is performed, it is called an experiment.
Outcome:
The result of the performance of an experiment is called an outcome.
Sample space:
The collection of all outcomes for an experiment is called a sample space.
Simple event:
A simple event is an event that includes one and only one of the final outcomes of an experiment.
Compound event:
A compound event is an event that includes more than one of the final outcomes of an experiment.
4.3
The experiment of selecting two items from the box without replacement has the following six possible outcomes:
AB
,
AC
,
BA
,
BC
,
CA
,
CB
.
Hence, the sample space is written as
S =
{
AB, AC, BA, BC, CA, CB
}
4.5
Let:
L
= person is computer literate
I =
person is computer illiterate
The experiment has four outcomes:
LL, LI, IL,
and
II.
4.7
Let:
G
= the selected part is good
D
= the selected part is defective
The four outcomes for this experiment are:
GG, GD, DG,
and
DD
4.9
Let:
H
= a toss results in a head
and
T
= a toss results in a tail
Thus the sample space is written as
S
= {
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
}
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4.11
a.
{
LI, IL
}; a compound event
c.
{
II, IL, LI
}; a compound event
b.
{
LL, LI, IL
}; a compound event
d.
{
LI
}; a simple event
4.13
a.
{
DG, GD, GG
}; a compound event
c.
{
GD
}; a simple event
b.
{
DG, GD
}; a compound event
d.
{
DD, DG, GD
}; a compound event
4.15
The following are the two properties of probability.
1.
The probability of an event always lies in the range zero to 1, that is:
1
)
(
0
≤
≤
i
E
P
and
1
)
(
0
≤
≤
A
P
2.
The sum of the probabilities of all simple events for an experiment is always 1, that is:
∑
=
+
+
+
=
1
)
(
)
(
)
(
)
(
3
2
1
E
P
E
P
E
P
E
P
i
4.17
The following are three approaches to probability.
1.
Classical probability approach:
When all outcomes are equally likely, the probability of an event
A
is given by:
experiment
the
ub
outcomes
of
Number
Total
in
outcomes
of
Number
)
(
A
A
P
=
For example, the probability of observing a 1 when a fair die is tossed once is 1/6.
2.
Relative frequency approach:
If an event
A
occurs
f
times in
n
repetitions of an experiment, then
P
(
A
) is
approximately
f
/
n
.
As the experiment is repeated more and more times,
f
/
n
approaches
P
(
A
).
For example, if 510 of
the last 1000 babies born in a city are male, the probability of the next baby being male is approximately 510/1000
= .510
3.
Subjective probability approach:
Probabilities are derived from subjective judgment, based on experience,
information and belief.
For example, a banker might estimate the probability of a new donut shop surviving for two
years to be 1/3 based on prior experience with similar businesses.
4.19
The following cannot be the probabilities of events:
−.55,
1.56,
5/3,
and
−2/7
This is because the probability of an event can never be less than zero or greater than one.
4.21
These two outcomes would not be equally likely unless exactly half of the passengers entering the metal detectors set it
off, which is unlikely.
We would have to obtain a random sample of passengers going through New York’s JFK airport,
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 Fall '07
 Guggenberger
 Electoral College, Probability theory, iL

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