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Math331, Spring 2008
Instructor: David Anderson
Section 4.2 Homework Answers
Homework:
pgs. 150158 #’s 1, 4, 5, 6, 7, 16.
1. The possible values of
X
are
{
0
,
1
,
2
,
3
,
4
,
5
}
. To Fnd the probabilities of each, we note that
all combinations of rolls in the sample space
S
=
{
(
a, b
)

a, b
∈ {
1
,
2
,
3
,
4
,
5
,
6
}}
are equiprob
able. So we need to count the number of ways to get each of the values in
{
0
,
1
,
2
,
3
,
4
,
5
}
,
and divide by 36. To get 0, both die must be the same. Therefore, there are exactly 6 ways
of doing this. So
P
{
X
= 0
}
= 6
/
36 = 1
/
6. To have
X
= 1, we think in the following way. If
the Frst roll is a 2, 3, 4, or 5, there are always two rolls possible on the second roll that gives
us
X
= 1. However, if the Frst roll is 1 or 6, there is only one possibility for the second roll.
Thus,
P
{
X
= 1
}
= 10
/
36. Similarly, if the Frst roll is a 3 or 4, there are two possibilities for
the second roll that gives
X
= 2, and a 1, 2, 5, or 6 gives only one possibility for the second
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This note was uploaded on 03/31/2008 for the course MATH 331 taught by Professor Anderson during the Spring '08 term at Wisconsin.
 Spring '08
 Anderson
 Math, Probability

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