9. A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician, hired by the company to investigate the level of contamination in the stored cartridges, found that 23% of the cartridges in a particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let Y = y be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for is given by the formula: p(y)=(0.23)(0.77)"*, y=1,2,3.. a) Find p(1). Interpret this result. b) Find p(5). Interpret this result.
9. A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician, hired by the company to investigate the level of contamination in the stored cartridges, found that 23% of the cartridges in a particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let Y = y be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for is given by the formula: p(y)=(0.23)(0.77)"*, y=1,2,3.. a) Find p(1). Interpret this result. b) Find p(5). Interpret this result.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please answer 9 and 10
![7. A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the
coins at random, and when he flips it, it shows heads.
a) What is the probability that it is the fair coin?
b) Suppose that he flips the same coin a second time and again it shows heads.
Now what is the probability that it is the fair coin?
c) Suppose that he flips the same coin a third time and it shows tails. Now what
is the probability that it is the fair coin?
8. Entomological engineers are continually searching for new biological agents to
control one of the world's worst aquatic weeds, the water hyacinth. An insect that
naturally feeds on water hyacinth is the delphacid. Female delphacids lay anywhere
from one to four eggs onto a water hyacinth blade. The Annals of the Entomological
Society of America (Jan. 2005) published a study of the life cycle of a South American
delphacid species. The accompanying table gives the percentages of water hyacinth
blades that have one, two, three, and four delphacid eggs.
One Egg
Two Egg
Three Egg
Four Egg
Percentage of
Blades
40
54
4
Source: Sosa, A. J., et al. “Life history of Megamelus scutellaris with description of immature stages,"
Annals of the Entomological Society of America, Vol. 98, No. 1, Jan. 2005 (adapted from Table 1).
a) One of the water hyacinth blades in the study is randomly selected and Y, the
number of delphacid eggs on the blade, is observed. Give the probability
distribution of Y.
b) What is the probability that the blade has at least three delphacid eggs?
9. A weapons manufacturer uses a liquid propellant to produce gun cartridges. During
the manufacturing process, the propellant can get mixed with another liquid to
produce a contaminated cartridge. A University of South Florida statistician, hired by
the company to investigate the level of contamination in the stored cartridges, found
that 23% of the cartridges in a particular lot were contaminated. Suppose you
randomly sample (without replacement) gun cartridges from this lot until you find a
contaminated one. Let Y= y be the number of cartridges sampled until a contaminated
one is found. It is known that the probability distribution for is given by the formula:
p(y)=(0.23)(0.77)"",
y = 1, 2, 3,...
a) Find p(1). Interpret this result.
b) Find p(5). Interpret this result.
2/3
10. The amount of time Y (in minutes) that a commuter train is late is a conumuvuv
random variable with probability density
(25 – y) if -5<y<5
f (y)={500'
elsewhere
[Note: A negative value of Y means that the train is early.]
a) Find the value of c for this probability distribution.
b) What is the probability that the train is no more than 3 minutes late?
End -
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Transcribed Image Text:7. A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the
coins at random, and when he flips it, it shows heads.
a) What is the probability that it is the fair coin?
b) Suppose that he flips the same coin a second time and again it shows heads.
Now what is the probability that it is the fair coin?
c) Suppose that he flips the same coin a third time and it shows tails. Now what
is the probability that it is the fair coin?
8. Entomological engineers are continually searching for new biological agents to
control one of the world's worst aquatic weeds, the water hyacinth. An insect that
naturally feeds on water hyacinth is the delphacid. Female delphacids lay anywhere
from one to four eggs onto a water hyacinth blade. The Annals of the Entomological
Society of America (Jan. 2005) published a study of the life cycle of a South American
delphacid species. The accompanying table gives the percentages of water hyacinth
blades that have one, two, three, and four delphacid eggs.
One Egg
Two Egg
Three Egg
Four Egg
Percentage of
Blades
40
54
4
Source: Sosa, A. J., et al. “Life history of Megamelus scutellaris with description of immature stages,"
Annals of the Entomological Society of America, Vol. 98, No. 1, Jan. 2005 (adapted from Table 1).
a) One of the water hyacinth blades in the study is randomly selected and Y, the
number of delphacid eggs on the blade, is observed. Give the probability
distribution of Y.
b) What is the probability that the blade has at least three delphacid eggs?
9. A weapons manufacturer uses a liquid propellant to produce gun cartridges. During
the manufacturing process, the propellant can get mixed with another liquid to
produce a contaminated cartridge. A University of South Florida statistician, hired by
the company to investigate the level of contamination in the stored cartridges, found
that 23% of the cartridges in a particular lot were contaminated. Suppose you
randomly sample (without replacement) gun cartridges from this lot until you find a
contaminated one. Let Y= y be the number of cartridges sampled until a contaminated
one is found. It is known that the probability distribution for is given by the formula:
p(y)=(0.23)(0.77)"",
y = 1, 2, 3,...
a) Find p(1). Interpret this result.
b) Find p(5). Interpret this result.
2/3
10. The amount of time Y (in minutes) that a commuter train is late is a conumuvuv
random variable with probability density
(25 – y) if -5<y<5
f (y)={500'
elsewhere
[Note: A negative value of Y means that the train is early.]
a) Find the value of c for this probability distribution.
b) What is the probability that the train is no more than 3 minutes late?
End -
The only way
to learn
mathematics
is to do
mathematics.
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