Answer Key to Assignment #2
Exercise 4.14 (4.5)
A:
rate of return will be more than 10%
B:
rate of return will be negative
a)
P(A) = 0.33 + 0.21 =
0.54
b)
P(B) = 0.04 + 0.14 =
0.18
c)
A
: rate of return will be
less than or equal to 10%
d)
P(
A
) = 1 – P(A) =
0.46
e)
B
A
:
rate of return will be both more than 10% as well as negative = Empty set
f)
P(
B
A
) = 0, being an empty set
g)
B
A B
: rate of return will be either
more than 10% or negative or both
h)
P(
B
A B
) = P(A) + P(B) –P(
B
A
) = 0.54 + 0.18 – 0 =
0.72
i)
Yes, since there is no rate of return that are common in events A and B, that is P(
B
A
) = 0
j)
No, because
1
)
(
≠
B
A
P
B
, that is the two events are not mutually exhaustive and
they do not cover the entire sample space
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Exercise 4.38 (4.21)
Define
EP:
a senior concerned about employment prospects; P(EP) = 0.30
G:
a senior concerned about grades; P(G) = 0.25
Also,
20
.
0
)
(
=
G
EP
P
G
EP B
: a senior is concerned about at least one, that is,
either EP or G, or both.
35
.
0
20
.
0
25
.
0
30
.
0
)
(
)
(
)
(
)
(
=

+
=

+
=
G
EP
P
G
P
EP
P
G
EP
P
°
Exercise 4.27 (4.44)
Define
WT:
an adult watches television program; P(WT) = 0.18
RP:
an adult reads publications; P(RP) = 0.12
12
.
0
)
(
=
RP
WT
P
a) To find:
?
)
/
(
=
WT
RP
P
WT
T
W
RP
0.10
0.02
0.12
P
R
0.08
0.80
0.88
0.18
0.82
1.00
56
.
0
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 Spring '08
 Chattopadhyay
 Probability theory, NS, FP, entire sample space

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