Question

A certain article manufactured in our facilities may present three different types of defects: minor aesthetic, major aesthetic and functional. Of the last 430 items manufactured, 46 have a minor cosmetic defect, 18 have a major cosmetic defect and 11 have a functional defect Only 3 of the 430 present the three types of defect, while 67 present at least one of aesthetic defects. 9 articles with major aesthetic defect and functional defect were identified, while there were 4 articles with minor aesthetic defect and functional defect. Calculate the probability of: a) Randomly select an item without defect b) The probability of selecting an item with both types of aesthetic defects c) If you select an item and it turns out that it has a minor aesthetic defect, what is the probability that it also has a functional defect?

Answer #1

A certain article manufactured in our facilities may present
three different types of defects: minor aesthetic, major aesthetic
and functional. Of the last 650 manufactured items, 69 have a minor
cosmetic defect, 26 have a major cosmetic defect and 17 have a
functional defect
Only 4 of the 650 present the three types of defect, while 101
present at least one of the aesthetic defects. Thirteen articles
with major cosmetic defect and functional defect were identified,
while there were 6...

A certain article manufactured in our facilities may present
three different types of defects: minor aesthetic, major aesthetic
and functional. Of the last 1,000 manufactured items, 105 have a
minor cosmetic defect, 40 have a major cosmetic defect, and 25 have
a functional defect.
Only 5 of the 1000 present the three types of defect, while 155
present at least one of the aesthetic defects. Twenty articles with
major cosmetic defect and functional defect were identified while
there were 8...

An article has 3 defects: minor aesthetic, major aesthetic and
functional. Of the last 480 articles, 51 have minor aesthetic
defects, 20 major aesthetic defects and 12 functional defects.
Only 3 of the 480 present the three types of defect, while 75
show at least one of the aesthetic defects. 10 articles with major
cosmetic defect and functional defect were identified, while there
were 4 articles with minor cosmetic defect and functional
defect.
Calculate the probability of:
a) Randomly select...

A certain system can experience three different types of
defects. Let Ai (i = 1,2,3) denote the
event that the system has a defect of type i. Suppose that
the following probabilities are true.
P(A1) = 0.11
P(A2) = 0.06
P(A3) = 0.04
P(A1 ∪
A2) = 0.14
P(A1 ∪
A3) = 0.13
P(A2 ∪
A3) = 0.08
P(A1 ∩
A2 ∩ A3) = 0.01
(Round your answers to two decimal places.)
(a) Given that the system has a type...

A certain system can experience three different types of
defects. Let Ai (i = 1,2,3) denote the event that the system has a
defect of type i.
Suppose that P(A1) = 0.25, P(A2) = 0.29, P(A3) = 0.33,
P(A1 ∪ A2) = 0.5, P(A1 ∪ A3) = 0.53, P(A2 ∪ A3) = 0.54,
P(A1 ∩ A2 ∩ A3) = 0.02
(a) Find the probability that the system has exactly 2 of the 3
types of defects.
(b) Find the probability...

A certain system can experience three different types of
defects. Let Ai (i = 1,2,3) denote the
event that the system has a defect of type i. Suppose that
the following probabilities are true.
P(A1) =
0.16 P(A2)
=
0.10 P(A3)
= 0.08
P(A1 ∪ A2) =
0.18 P(A1
∪ A3) = 0.19
P(A2 ∪ A3) =
0.14 P(A1
∩ A2 ∩ A3) = 0.02
(a) What is the probability that the system does not have a type
1 defect?
(b) What is the...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
Save
Share
8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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