Statistical Analysis Quiz 1
Section : 510.601.52
In a recent survey of Baltimore homes, 10% of the homes have a deck and 52% have a parking space. Suppose
91% of the homes with a deck also have a parking space.
a.
What percent of homes have a deck and a parking space? (3 points)
P
(
P∩ D
)
=
P
(
P

D
)
P
(
D
)
=
0.91
∗
0.1
=
0.091
b.
What is the probability that a home has a deck or a parking space? (3 points)
P
(
P
∪
D
)
=
P
(
P
)
+
P
(
D
)
−
P
(
P∩ D
)
=
0.52
+
0.1
−
0.091
=
0.529
c. What is the probability that a home with a parking space has a deck? (4 points)
P
(
D

P
)
=
P
(
D∩ P
)
P
(
P
)
=
P
(
P

D
)
P
(
D
)
P
(
P
)
=
0.91
∗
0.1
0.52
d. Are the events "having a deck" and "having a parking space" independent? Why or why not? (3
points)
If independent,
P
(
P∩ D
)
=
P
(
P
)
∗
P
(
D
)
; P
(
P∩ D
)
=
0.091
; P
(
P
)
∗
P
(
D
)
=
0.52
∗
0.1
=
0.052
,
hence the
two are not independent
Statistical Analysis Quiz 1
Section : 510.601.F2 1
We observed fluctuations in the value of the US dollar against the Euro on 4 random days in 2014. On each of
the days, we took an equal number of measurements. On day 1, 2% of the measurements showed
depreciation of the dollar against the euro, 4% of measurements on day 2 showed depreciation, and 1% on day
3 while 6% of the measurements showed depreciation on day 4.
a.
If a certain measurement is selected from each day, what is the probability that the measurements
from days 1 and 2 showed depreciation and from days 3 and 4 did not show depreciation? (3 points)
P
(
1
∩
2
∩
´
3
∩
´
4
)
=
0.02
∗
0.04
∗
0.99
∗
0.94
b.
What is the probability that a randomly selected measurement is from day 2 and showed depreciation?
(3 points)
P
(
Depreciation∩
2
)
=
P
(
Depreciation

2
¿
P
(
2
)
=
0.04
∗
0.25
c.
If a randomly selected measurement showed depreciation, what is the probability that it came from
day 2? (4 points)
P
(
Depreciation

2
P
(
Depreciation

1
P
(
2

Depreciation
)
=
¿
P
(
2
)
¿
¿
P
(
1
)
+
P
(
Depreciation

2
¿
P
(
2
)
+
P
(
Depreciation

3
¿
P
(
3
)
+
P
(
Depreciation

4
¿
P
(
4
)
¿
=
0.02
2. Four sixsided dice are rolled. What is the probability that the numbers they show are all different? (3 points)
6
(
withoutrepitition
)
P
4
6
(
repitition
)
=
6
!
2
!
6
4
the days, we took an equal number of measurements. On day 1, 2% of the measurements showed
depreciation of the dollar against the euro, 4% of measurements on day 2 showed depreciation, and 1% on day
3 while 6% of the measurements showed depreciation on day 4.
a.
If a certain measurement is selected from each day, what is the probability that the measurements
from days 1 and 2 did not show depreciation and from days 3 and 4 showed depreciation? (3 points)
P
(
´
1
∩
´
2
∩
3
∩
4
)
=
0.98
∗
0.96
∗
0.01
∗
0.06
b.
What is the probability that a randomly selected measurement is from day 3 and showed depreciation?
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