Math 431 First Evening Exam
Room B239, 6:00pm  7:00pm, February 18, 2005
M´arton Bal´azs
NAME:
1.
My friend Bob takes the Madison  Nowheretown flight with Windy Airlines today, and I’ll
fly the same flight tomorrow. This airline has three types,
A
,
B
and
C
, of planes, with 3, 4, and
6 seats per row, respectively. We know that the same plane flies to Nowheretown every day, but
we don’t know of which type this plane is, so we estimate it could be each of the three types
A
,
B
or
C
with equal chance. We also know that seats are assigned completely randomly to
passengers.
(a)
(15 points) What is the probability that I will have a window seat tomorrow?
Answer:
2
3
·
1
3
+
2
4
·
1
3
+
2
6
·
1
3
=
1
2
.
(b)
(15 points) Later Bob tells me that he had a window seat. Then what is the probability
that plane type
A
,
B
, or
C
, respectively, is the one to fly to Nowheretown?
Answer:
2
3
·
1
3
1
2
=
4
9
,
2
4
·
1
3
1
2
=
1
3
and
2
6
·
1
3
1
2
=
2
9
, respectively.
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 Fall '05
 BALAZS
 Math, Probability, Probability theory, window seat

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