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11.4 Probability
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11.4 Probability

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  • 1. 11.4 Fundamentals of Probability
  • 2. Some important questions
    What is probability?
    Why study probability?
    What is the probability of winning the Maryland lottery?
    What is the probability of being struck by a lightning?
    What is the probability of getting an A in the class?
  • 3. Computing Theoretical Probability
    If an event E has n(E) equally-likely outcomes and its sample space S has n(s) equally-likely outcomes, the theoretical probability of event E, denoted by P(E) is
    P(E) = number of outcomes in event E = n(E)
    total # of possible outcomes n(S)
  • 4. Example 1
    A die is rolled once. Find the probability of getting:
    a. 5
    b. an even number
    c. a number greater than 2
    d. a number less than 6
    e. a number greater than 4
  • 5. Example 2
    You are dealt a standard 52-card deck. Find the probability of being dealt
    A. A king
    B. A red card
    C. A five
    D. A picture card
    E. A red queen
    F. A club
  • 6. Probabilities in Genetics
    Blood type problem: What is the chance of having a blood type AB if your parents have types AO and BB.
    Dimples: Facial dimples are examples of dominant genes which means that if a person has genotype DD or Dd, he or she will have a dimple. A person with no dimple has a genotype of dd. What is the chance of producing an offspring with a dimple if one parent has a dimple and the other has none?
  • 7. Empirical Probability
    Theoretical probability is based on a set of equally-likely outcomes and the number of elements in a set. By contrast, empirical probability applies to situations in which we observe the frequency of occurrence of an event.
    P (E) = observed number of times E occurs
    total number of observed occurences
  • 8. Example
    Marital Status of the US Population , Ages 18 or older in millions
    Source: US Census Bureau
  • 9. Questions:
    What is the probability of randomly selecting a female?
    What is the probability of randomly selecting a divorced person?
    What is the probability of randomly selecting a married male?
  • 10. Assignments
    Classwork: Checkpoints 1-4 p. 580-584
    And do #s 2-30 (evens)
    HW: p. 585-586, #s 1-39 (odd); 49-63 (odd)