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Probability Summary

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What Do We Know So Far?

  • Write down everything we know about probability

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What Do We Know So Far?

  • Sets and Venn Diagrams
  • Probability by counting
  • Probability by Venn Diagrams
  • Conditional Probability
  • Dependent and Independent events

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Example Sets

  • Given: Find:

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Example Sets

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Example Venn Diagrams

  • Diagram

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Example Venn Diagrams

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Example Venn Diagrams

  • What does the diagram represent?

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Example Venn Diagrams

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Example Basic Probability

  • Given a fair coin, what is the probability of getting at least 2 heads with three flips?

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Example Basic Probability

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Example Basic Probability with Trees

  • A bag has 3 blue marbles, 2 red marbles and 4 yellow marbles
  • Two marbles are drawn in succession with no replacement
  • Draw a tree diagram that represents this situation
  • Find:
    • P(both blue)
    • P(one blue, one yellow)
    • P(at least one red)
    • P(same colour)

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Example Basic Probability with Trees

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Principle of Inclusion and Exclusion

  • Given events A, B then

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Example Inclusion and Exclusion

  • A student has a ⅔ probability of passing math and 4/9 probability of passing English
  • The probability of passing any subject is ⅘
  • What is the probability of passing both subjects?

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Example Inclusion and Exclusion

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Conditional Probability and Independent Events

  • Conditional probability:
    • C has happened
    • What is probability that E happens?

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  • Two events A, B are independent if or if

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  • The events are dependent if they are not independent

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Example Conditional Probability and Independence

  • Given P(A)=0.6, P(B) = 0.7 and A, B are independent
  • Find

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Example Conditional Probability and Independence

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Credits

Special thanks to all the people who made and released these awesome resources for free:

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  • Presentation template by SlidesCarnival
  • Photographs by Startupstockphotos

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