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MATH S104 Lecture 10 Inclass Problem Solutions
July 23, 2009
Problem 1
*
:
a) Find the probability of rolling at least one six when a die is rolled four times.
The number of ways that a nonsix can be rolled four times is 5
4
. The total number
of ways that one die can be rolled four times is 6
4
. Thus, the probability that
no
six
is rolled is
5
4
6
4
, so the probability that at least one six is rolled is
1

5
4
6
4
=
6
4

5
4
6
4
=
671
1296
=
0
.
517
b) Find the probability that at least one six or at least one one is rolled when a die is rolled
four times.
Let
S
1
be the set of 4roll instances with at least one one, and let
S
6
be the set of 4roll
instances with at least one six. We are interested in
±
S
1
∪
S
6
±
, the size of the set with
at least one one or at least one six. It is easier to compute the set of 4roll sequences
with no ones or sixes:
±
(
S
1
∪
S
6
)±
=
4
4
Since there are 6
4
total 4roll instances, the probability of getting an instance that
does
have either a one or a six is:
±
S
1
∪
S
2
±
=
6
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