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More Probability Examples (Probability Reviewed)
Example 1
Each of a sample of four home mortgages is classi…ed as …xed rate (
F
) or variable rate (
V
).
a.
What are the 16 outcomes in
S
?
Solution
S
=
{
FFFF
,
FFFV
,
FFV F
,
FV FF
,
FV FV
,
FV V F
,
FV V V
,
V FFF
,
V FFV
,
V FV F
,
V FV V
,
V V FF
,
V V FV
,
V V V F
,
V V V V
}.
b.
Which outcomes are in the event that exactly three of the selected mortgages are a …xed rate?
Solution
A
=
{
FFFV
,
FFV F
,
FV FF
,
V FFF
}.
c.
Which outcomes are in the event that all four mortgages are of the same type?
Solution
B
=
{
FFFF
,
V V V V
}.
d.
Which outcomes are in the event that at most one of the four is a variablerate mortgage?
Solution
C
=
{
FFFF
,
FFFV
,
FFV F
,
FV FF
,
V FFF
}.
e.
What are the union and intersection of the two events in parts
b
and
d
?
Solution
A
[
C
=
{
FFFV
,
FFV F
,
FV FF
,
V FFF
,
FFFF
,
V V V V
};
A
\
C
=
A:
f.
What are the union and intersection of the two events in parts
c
and
d
?
Solution
B
[
C
=
{
FFFV
,
FFV F
,
FV FF
,
V FFF
,
FFFF
,
V V V V
};
B
\
C
=
{
FFFF
}.
Example 2
A construction …rm is working on two di¤erent projects. Let
A
be the event that the
…rst one is completed by the contract date and de…ne
B
analogously for the second project.
If
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This note was uploaded on 01/08/2012 for the course EXST 4050 taught by Professor Staff during the Fall '10 term at LSU.
 Fall '10
 Staff

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