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ORIE 3500/5500 Fall Term 2008
Assignment 2Solution
1. Let
A
1
,A
2
and
A
3
be the events that ﬁrst, second and third friend hit
the deer respectively. They are independent and
P
(
A
1
) = 0
.
3
,P
(
A
2
) = 0
.
4
,P
(
A
3
) = 0
.
5
.
(a)
P
(
A
1
∩
A
2
∩
A
3
) =
P
(
A
1
)
P
(
A
2
)
P
(
A
3
) = 0
.
3
×
0
.
4
×
0
.
5 = 0
.
06
.
(b) The required probability is
P
(
A
1
∩
A
2
∩
A
c
3
) +
P
(
A
1
∩
A
c
2
∩
A
3
) +
P
(
A
c
1
∩
A
2
∩
A
3
)
=
P
(
A
1
)
P
(
A
2
)
P
(
A
c
3
) +
P
(
A
1
)
P
(
A
c
2
)
P
(
A
3
) +
P
(
A
c
1
)
P
(
A
2
)
P
(
A
3
)
= 0
.
3
×
0
.
4
×
(1

0
.
5) + 0
.
3
×
(1

0
.
4)
×
0
.
5 + (1

0
.
3)
×
0
.
4
×
0
.
5
= 0
.
06 + 0
.
09 + 0
.
14 = 0
.
29
(c) Let
F
be the event that exactly one bullet hit the deer. Then
F
= (
A
1
∩
A
c
2
∩
A
c
3
)
∪
(
A
c
1
∩
A
2
∩
A
c
3
)
∪
(
A
c
1
∩
A
c
2
∩
A
3
) and
P
(
F
)
=
P
(
A
1
∩
A
c
2
∩
A
c
3
) +
P
(
A
c
1
∩
A
2
∩
A
c
3
) +
P
(
A
c
1
∩
A
c
2
∩
A
3
)
=
P
(
A
1
)
P
(
A
c
2
)
P
(
A
c
3
) +
P
(
A
c
1
)
P
(
A
2
)
P
(
A
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 Fall '08
 TODD

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