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STAT 400
Spring 2011
Homework #1
(due Friday, January 28, by 3:00 p.m.)
1.
Suppose that
P(A) = 0.40,
P(B) = 0.30,
P(A
∩
B) = 0.20.
What is the probability that …
a)
either A occurs or B occurs (or both);
b)
B does not occur;
c)
B occurs and A does not occur;
d)
neither A nor B occurs;
a)
P
(
A
∪
B
) =
0.50
.
b)
P
(
B
'
) =
0.70
.
c)
P
(
B
∩
A
'
) =
0.10
.
d)
P
(
A
'
∩
B
'
) =
0.50
.
2.
Suppose that
P
(
A
) = 0.40,
P
(
B
) = 0.50,
P
(
A
∪
B
) = 0.70.
Find …
a)
P
(
A
∩
B
);
b)
P
(
A
'
∩
B
'
);
c)
P
(
A
'
∪
B
'
).
a)
P
(
A
∪
B
) = P
(
A
) + P
(
B
) – P
(
A
∩
B
)
0.7 = 0.4 + 0.5 – P
(
A
∩
B
)
P
(
A
∩
B
) =
0.2
.
b)
P
(
A
'
∩
B
'
) = 1 – P
(
A
∪
B
) = 1 – 0.7 =
0.3
.
c)
P
(
A
'
∪
B
'
) = 1 – P
(
A
∩
B
) = 1 – 0.2 =
0.8
.
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Suppose
P
(
A
) = 0.6,
P
(
B
) = 0.5,
P
(
C
) = 0.4,
P
(
A
∩
B
) = 0.3,
P
(
A
∩
C
) = 0.2,
P
(
B
∩
C
) = 0.2,
P
(
A
∩
B
∩
C
) = 0.1.
Find …
a)
P
(
A
∪
B
);
b)
P
(
B
∪
C
);
c)
P
(
(
A
∪
B
)
∩
C
'
);
d)
P
(
A
∪
(
B
∩
C
)
).
a)
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
–
P
(
A
∩
B
)
=
0.6 + 0.5 – 0.3
=
0.8
.
b)
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 Spring '11
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