ENM 207

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ENM 207

• Lecture 7

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Example

• There are three columns entitled Art (A)
  ,Books (B) and Cinema (C) in a new magazine.
  Reading habits of a randomly selected reader with
  respect to choose columns are

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• What is the probability of reading A given that
  they are reading B or C columns?

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Example Mendenhall 3.63

• solution
• There are five suppliers and a company will
  choose at least 2 suppliers, therefore, we must
  find the number of ways to select 2, 3, 4 and 5
  suppliers from the 5.
• At least 2 means that , a company can choose 2 or
  3 or 4 or 5 suppliers from 5.
• The total number of obtions are

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Example3.65

• Define the following events
• (A) Part is supplied by company A
• B) Part is supplied by company B
• C) Part is defective
• From the problem, P(A)0.8, P(B)0.2,
• P(C\A) 0.05 , P(C\B) 0.03
• We know the given part is defective and we want
  to find
• The probability it come from company A
• And the probability it come from company B
• P(A\C)? , P(B\C)?

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Total Probability And Bayes Theorem

• Partitions Total Probability And Bayes Theorem
• A partition of the sample space may be defined
  like this.

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Total Probability Law
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Bayes Theorem

• Another important result of the total probability
  law is known as Bayes Theorem

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Ex 2.35 page 56 (Montgomery)
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Example

• Three machines A,B,C produce respectively 50,
  30, 20 of the total number of items of a
  factory .
• The percentages of defective output of these
  machines are 3 , 4 , 5,respectively. If an
  item is selected at random, find the probability
  that the item is defective.
• Let X be the event that an item is defective.
• Which theorem or which rule is used to solve this
  problem?
• Total probability law.

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Another way to solve this problem Tree Diagram
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Example

• Consider the factory in the preceeding example.
  Suppose an item is selected at random and is
  found to be defective. Find the probability that
  the item was produced by machine A
• What is the P(A\X)?
• Which theorem or which law can be used to solve
  this problem?

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Ex 4.11 p 62/schaums outline series

• In a certain college, 25 of the students failed
  math, 15 of the students failed chemistry, 10
  of the students failed both math and chemistry.
  A student is selected at random.
• a) If he failed chemistry what is the probability
  that he failed math?
• b) If he failed math, what is the probability
  that he failed chemistry?
• c) What is the probability that he failed math or
  chemistry?

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SYSTEM RELIABILITY

• System- electronic, mechanical or a combination
  of both are composed of components.
• A component of a system is represented by a
  capital letter.
• Two system each composed of tree components A B
  C are shown below.
• Systems according to their components connections
  can be classified in two groups. Such as series
  and parallel.

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Definition

• If the system fails when any of the components
  fails, it is called a series system.

• If the system fails only when all of its
  components fail, it is called
• a parallel system.

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This system is composed of five components A, B,
C, D and E as shown above. Components D and E
are from a two-component parallel system. This
subsystem is connected in series with A, B and
C.
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Summary of system reliability
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Example 17.22 First subcircuits involves comp.
A,B,C in parallel.
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