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Exam 1
(
Version A – white
)
(
Answers
)
1.
The population of Lilliput is divided into LittleEndians and BigEndians based
on which end of a boiled egg they believe should be opened.
Suppose that 60%
of Lilliputians are LittleEndians, and 40 % are BigEndians.
Suppose also that
16% of LittleEndians and 26% of BigEndians have blue eyes.
P( Little ) = 0.60,
P( Big ) = 0.40,
P( Blue
 Little ) = 0.16,
( 16% of LittleEndians
have blue eyes ),
P( Blue
 Big ) = 0.26.
( 26% of BigEndians
have blue eyes ).
a)
(4)
What proportion of Lilliput population have blue eyes?
Blue
Blue
'
Little
0.60
⋅
0.16
0.096
0.504
0.60
P( Blue
 Little ) = 0.16
Big
0.40
⋅
0.26
0.104
0.296
0.40
P( Blue
 Big ) = 0.26
0.20
0.80
1.00
OR
P( Blue )
=
P( Little )
⋅
P( Blue

Little ) + P( Big )
⋅
P( Blue

Big )
=
0.60
⋅
0.16 + 0.40
⋅
0.26
=
0.096 + 0.104
=
0.20
.
b)
(3)
You meet a Lilliputian with blue eyes.
What is the probability that he is a
LittleEndian?
P( Little  Blue ) =
20
.
0
096
.
0
)
Blue
(
P
)
Blue
Little
(
P
=
∩
=
0.48
.
c)
(3)
The first democratically elected Lilliputian president is a LittleEndian with blue
eyes.
His first day in office he proposed a tax break for Lilliputians who are
either LittleEndians or have blue eyes, or both. What proportion of the Lilliput
population would receive a tax break under his proposal?
P( Little
∪
Blue ) = P( Little ) + P( Blue ) – P( Little
∩
Blue )
= 0.60 + 0.20 – 0.096 =
0.704
.
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View Full Document2.
(3)
How many ways are there to rearrange letters in the word
MISSISSIPPI
?
11
letters:
4
I
,
1
M
,
2
P
,
4
S
.
!
!
!
!
!
4
2
1
4
11
⋅
⋅
⋅
=
34,650
.
OR
11
C
4
⋅
7
C
1
⋅
6
C
2
⋅
4
C
4
= 330
⋅
7
⋅
15
⋅
1 =
34,650
.
3.
(4)
In order to create more room in his freezer, Alex took all pizza pockets out of the
boxes, but he forgot to label them.
He only remembers that 5 are ham and cheese,
7 are pepperoni pizza, and 4 are Philly steak.
When a few of his friends drop over
for a game of poker, Alex decides to serve pizza pockets.
If he selects 5 pockets
at random, what is the probability that 2 of them are ham and cheese and 3 are
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 Spring '08
 STEPANOV
 Statistics

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