Statistics 427: Homework #2
Solutions to Assigned Problems
2.45
[10 pts (3,4,3)]
(a)
P
(
A
) = 0
.
106 + 0
.
141 + 0
.
200 = 0
.
447
P
(
C
) = 0
.
215 + 0
.
200 + 0
.
065 + 0
.
020 = 0
.
5
P
(
A
∩
C
) = 0
.
200
(b)
P
(
A

C
) =
P
(
A
∩
C
)
P
(
C
)
=
0
.
200
0
.
5
= 0
.
4
P
(
C

A
) =
P
(
C
∩
A
)
P
(
A
)
=
0
.
200
0
.
447
= 0
.
44742
P
(
A

C
) represents the probability that someone from ethnic group 3 has blood type A.
P
(
C

A
)
represents the probability that a person with blood type A is from ethnic group 3.
(c)
Let
D
=
{
ethnic group 1 selected
}
.
P
(
D

B
0
) =
P
(
D
∩
B
0
)
P
(
B
0
)
.
Now
P
(
B
) = 0
.
008 + 0
.
018 + 0
.
065 = 0
.
091 and so
P
(
B
0
) = 1

0
.
091 = 0
.
909. So
P
(
D

B
0
) =
P
(
D
∩
B
0
)
P
(
B
0
)
=
0
.
082 + 0
.
106 + 0
.
004
0
.
909
=
0
.
192
0
.
909
= 0
.
211
.
2.47
[10 pts (2,2,2,2,2)]
(a)
We know
P
(
A
) = 0
.
5,
P
(
B
) = 0
.
4, and
P
(
A
∩
B
) = 0
.
25. So
P
(
B

A
) =
P
(
A
∩
B
)
P
(
A
)
=
0
.
25
0
.
5
= 0
.
5
.
This means that 50% of Visa card holders have a MasterCard.
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 Spring '08
 Staff
 Statistics, 50%, 10 pts, MasterCard, Visa Inc., Visa card, 37.5%

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