Conditional Probability

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Conditional Probability
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Conditional Probability

• Denotes the probability of the event E given that
  the event F is known to have occurred.
• To compute the conditional probability use

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Conditional Probability

• My dog loves jelly beans. So, I buy two bags at
  the Jelly Beanery and mix them together in her
  treat jar. The following table is a break down
  of the flavors (colors) in each bag.

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Conditional Probability

• Lets define the following events
• A event that a red bean is selected from the
  treat jar.

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Conditional Probability

• Lets define the following events
• B event that a brown bean is selected from the
  treat jar.

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Conditional Probability

• Lets define the following events
• C event that the selected bean was from bag 1.

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Conditional Probability

• Lets define the following events
• D event that the selected bean was from bag 2.

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Conditional Probability

• Lets say that we pull a brown bean from the
  treat jar (given). What is the probability that
  it came from bag 1?

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Conditional Probability

• Lets say that we pull a red bean from the treat
  jar (given). What is the probability that it
  came from bag 2?

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Conditional Probability Example

• A GFI switch will turn off power to a system in
  the event of an electrical malfunction. A spa
  manufacturer currently has 25 spas in stock, each
  equipped with a single GFI switch. The switches
  are supplied by two different companies, and some
  of them are defective, as summarized in the
  following table.

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Conditional Probability Example

• A spa is randomly selected for testing. Let
• E event that GFI switch in selected spa is
• from company 1
• F event that GFI switch in select spa is
  defective

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Conditional Probability Example

• Now suppose that testing reveals a defective
  switch. How likely is it that the switch came
  from the first company?

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Homework

• Section 6.4
• 6.29
• 6.30 Great mechanics question
• 6.32 Great concept question
• 6.33-6.35