1
Dr. V.R. Bencivenga
Economics 329
PRACTICE HOMEWORK #4A:
PROBABILITY
1.
Hydraulic landing assemblies coming from an aircraft rework facility are inspected for defects.
Historical records indicate that 8% have defects in shafts only, 6% have defects in bushings only,
and 2% have defects in both.
One of the hydraulic assemblies is selected at random.
What is
the probability the assembly has
a.
a bushing defect
b.
a shaft or bushing defect
c.
exactly one of the two types of defects
d.
neither type of defect
2.
In a game, a player is given three attempts to hit a ball.
On each attempt, she either scores a hit
(H) or a miss (M).
The game requires the player to alternate which hand she uses, i.e., she can
make three attempts using RLR or LRL.
Her chance of scoring a hit with her right hand is .7 and
with her left hand is .3, so she starts with her right hand (RLR).
Results of successive attempts
are independent.
She wins if she scores at least two hits in a row.
a.
Give the sample space generated by this experiment.
What is the probability distribution
over the sample space?
b.
What is the probability she wins the game?
3.
Consider an experiment in which five fibers, which have lengths one, two , three, four, and five
inches, respectively, are tested to see which breaks first.
Suppose that the probability that any
given fiber will break first is proportional to the length of that fiber.
Give the sample space, and
the probability distribution over the sample space.
4.
A publisher has six textbooks in physics in its catalog.
The publisher is deciding on its advertising
strategy regarding these textbooks.
Each textbook can be advertised, or not.
Think of this
decision as a random trial.
a.
How many distinct outcomes are possible?
b.
Of these outcomes, in how many are four or more of the physics textbooks advertised?
c.
A marketing specialist is hired to rank the six texts according to projected sales over the
next two years.
How many distinct rankings are possible?
d.
The publisher decides to commission new editions of three of the six physics textbooks,
one in each of the next three years.
The marketing specialist is asked to choose three
texts for new editions, specifying the text to be updated in the first year, the text to be
updated in the second year, and the text to be updated in the third year.
How many
distinct rankings are possible?
e.
The publisher decides that it will begin an annual mailing to physics professors of an
advertising pamphlet that focuses on three of its six physics texts.
The company does not
want to focus on the same three texts more than once.
It does not mind repeating one
or two of them, but it does not want all three to be the same as in a previous mailing.
How many years can the publisher stick to this policy before it is forced to change it?
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 Spring '12
 BENCIVENGA
 Economics, Probability, Nobel Prize

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