University of Wisconsin
February 15, 2008
Math 331
Test 1
Name:
Answer Key
1. Legibly print your name above.
2. Do not open this test booklet until you are directed to do so.
3. Budget your time wisely!
4. This test is closed book and closed notes.
You will have until 2:10PM to complete the
exam. If you finish early you may leave. However, I would recommend you go back and
check your work.
5. Throughout the test,
show your work so that your reasoning is clear
.
Otherwise
no credit will be given.
6. Do not spend too much time on any one problem. Read them all through first and attack
them in the order that allows you to make the most progress. Repeat: Budget your time
wisely!
7. If you need extra room, use the back of the pages. Just make sure I can follow your work.
8. Sign the honor pledge when you are done. Good luck!
Problem
Points
Grade
1
12
2
10
3
7
4
10
5
16
6
16
7
14
Total
85
1
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1. (12 pts) For each of the following, give a sample space for the experiment described. Also,
define the event asked for. Be very clear!
(a) (4 pts.) You roll a four sided die and a six sided die once each. The event you are
interested in is getting a 4 with the four sided die.
S
=
{
(
a,b
)

a
∈ {
1
,
2
,
3
,
4
}
,b
∈ {
1
,
2
,
3
,
4
,
5
,
6
}}
E
=
{
(4
,b
)

b
∈ {
1
,
2
,
3
,
4
,
5
,
6
}}
(b) (4 pts.) You roll a four sided die until a 4 comes up. The event you are interested in
is getting a three with the first two rolls.
S
=
{
a
1
a
2
· · ·
a
n

n
≥
1
,a
n
= 4
,a
i
∈ {
1
,
2
,
3
}
for
i
negationslash
=
n
}
E
=
{
33
a
3
a
4
· · ·
a
n

n
≥
3
,a
n
= 4
,a
i
∈ {
1
,
2
,
3
}
for
i
negationslash
=
n
}
(c) (4 pts.) A cab has a single passenger that will be dropped off to one of three hotels.
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 Spring '08
 Anderson
 Math, Probability, Probability theory, pts

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