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UF ESI 6321
PreWark Assignment
Due August
17, 2007
Luther Setzer
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UFESI632I
7/11/2007
21.
A foursided die is engraved with the numbers
1 through 4 on its four different sides.
Suppose that when rolled, each side (and hence each number) has an equal probability of being the
bottom face when it lands.
We roll two such dice.
Let X be the sum of the numbers on the bottom
face of the two dice.
(a) What is the probability that X is at least five?
Listing the possible combinations
of the two dice:
I
1
1 2
1 3
14
2 I
22
23
24
3 I
32
33
34
41
42
43
44
This yields 16 possiblities.
Ten have the sum of five or greater.
Thus,
10116= 5/8
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(b) How does your answer to (a) change if you are told that the bottom face of
the first
die
has the
number "3" on it?
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If the bottom number is three then the first die that means the only combinations
you can count are the ones that
have 3 as the first number.
3/16
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(c) How does your answer to (a) change if you are told that the bottom face
ofone
of the dice
has
the number "3" on it?
This Would~be
3116 for the same reason as (b)~
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Luther Setzer
I NASA Pkwy EStop
NEM3, Kennedy Space Center, FL 32899
(321) 5447435
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UFESI632I
7/11/2007
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25.
In
Oblako County, any day can be either sunny or cloudy.
•
If a day is sunny, the following day will be sunny with probability 0.60.
•
If a day is cloudy, the following day will be cloudy with probability 0.70.
Suppose it is cloudy on Monday.
(a) What is the probability that it will be sunny on Wednesday?
PTuesday
_sunny= 0.30
PWednesday_sunny
=
0.39
~
...

(b) What is the probability that it will be sunny on both Tuesday and Wednesday?
Luther Setzer
I NASA Pkwy EStop
NEM3, Kennedy Space Center, FL 32899
(321) 5447435
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UFESI632I
7/11/2007
27.
It is a relatively rare event that a new television show becomes a longterm success.
A new television show that is introduced during the regular season has a 10% chance of becoming
a longterm success.
Pregular_success:=
10%
A new television show that is introduced as a midseason
replacement
has only a 5% chance of
becoming a longterm success.
Approximately
60% of all new television shows are introduced during the regular season.
Pregular_new :=
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