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Homework 2 solution (Fall, 2007)
2.3.1
3 Let
Sh
denote ”Shock resistance” and
Sc
denote ”Scratch resistance”. Let the subscript
h
denote ”High resistance” and
l
denote ”Low resistance”.
i.
S
=
{
Sh
h
Sc
h
,Sh
h
Sc
l
,Sh
l
Sc
h
,Sh
l
Sc
l
}
ii.
{
Sh
l
Sc
h
,Sh
l
Sc
l
}
. There are 14 disks such like that.
iii.
{
Sh
h
Sc
l
,Sh
l
Sc
h
,Sh
l
Sc
l
}
. There are 30 disks such like that.
5
i.
P
(
A
∪
B
) = 0
.
6
ii.
P
(
A

B
) =
p
(
A
)

p
(
A
∩
B
) = 0
.
4

0
.
1 = 0
.
3
iii.
P
(
A
∩
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∪
B
) = 0
.
4 + 0
.
3

0
.
6 = 0
.
1
2.4.1
1.
P
(
A
) =
P
(Machine A produce a batch with no defectives) = 0
.
95
P
(
B
) =
P
(Machine A produce a batch with no defectives) = 0
.
92
P
(
A
∩
B
) =
P
(Both machine A and machine B produce a batch with no defectives) = 0
.
88
i.
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) = 0
.
95 + 0
.
92

0
.
88 = 0
.
99
ii.
P
(
A
∪
B
)

P
(
A
∩
B
) = 0
.
99

0
.
88 = 0
.
11
4.
i.
P
(
S
) =
P
(1)+
P
(2)+
P
(3)+
P
(4)+
P
(5)+
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This note was uploaded on 07/17/2008 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.
 Fall '00
 Akritas

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