Statistics Chapter 4: Probabilities

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honestkyle
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198145
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Statistics Chapter 4: Probabilities
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2013-04-11 12:16:32
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probability events factorals permutations stats
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Probability
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  1. What is the definition of probability?
    The chance of likelihood of an event occurring
  2. What is the sample space?
    The set of all possible outcomes of an experiment or situation
  3. How do you represent the sample space for a coin?
    S = {Head, Tail}
  4. How do you represent the sample space for a die?
    S = {1, 2, 3, 4, 5, 6}
  5. What are events?
    • Collection of outcomes or sample points resulting from an experiment
    • Example: Roll a die (experiment) and get a 3 (event A). A = {3}
    • Example: Roll a die (experiment) and get a number > 3 (event B). B = {4, 5, 6}
  6. What is the classical method of assigning properties?
    • Assigning based on the assumption of equally likely outcomes
    • All the same weight
  7. How do you assign probabilities in terms of long-run relative frequency?
    Assigning based on experimentation or historical values
  8. How do you assign probabilities subjectively?
    Asses based on judgement, experience, expertise, or intuition
  9. What is the difference between probability and uncertainty?
    • Probability means knowing the likelihood of something occuring
    • Uncertainty means you can't even guess what the outcome or value will be
  10. What are the limits of a probability value?
    0 and 1
  11. What must the sum of all probabilities in an experiment equal?
    1
  12. In the Classical Method, if an experiment has n possible outcomes, what is the probability of each?
    1/n
  13. What is the counting rule for multi-step experiments?
  14. For an experiment involving a coin flipped 3 times, how would you show that in probabilities?
    (2)(2)(2) = 8 possible outcomes
  15. How is factorial represented?
    • !n
    • factorial of 4 = !4
  16. What is the equation for Counting Rule Combinations?
  17. What is the equation for Counting Rules Permutations?
  18. What happens when then number of permutations can repeat in counting rules?
    • The number of permutations becomes exponential
    • Example: Set a password with 8 characters, case sensitive, plus numbers
    • Total options = 62
    • Total draws = 8
  19. What is the Relative Frequency Method of probabilities?
    • Assigning probabilities based on historical data
    • Things you noticed in the past
  20. What is the Subjective Method of assigning probabilities?
    When you assign based on some historical data and a degree of personal belief in what will occur.
  21. What is the Complement of an Event?
    • It's a probability event of all the sample points that WILL NOT occur in another event.
    • S = {1,2,3,4,5,6}
    • A = {3}
    • Ac = {1,2,4,5,6}
  22. What are the notations for a Complement of an Event?
    • Ac
    • A1
  23. What is the Complement of an Event equation?
    P(Ac) = 1 - P(A)
  24. What is the Union of 2 Events?
    • The event containing all sample points that are in A OR B OR Both
    • OR
    • A = {3,4,5,6} B = {2,3,4}
    • = {2,3,4,5,6}
  25. What is the notation for Union of 2 Events?
    • A or B
  26. What is the Intersection of 2 Events?
    • The set of all sample points that are in both A AND B
    • AND
    • A = {3,4,5,6} B = {2,3,4 }
    • {3,4}
    • 2/6
  27. What is the notation for the Intersection of 2 Events?
    • A and B
    • junction
  28. What is Addition Law?
    It's used to compute the probability of the union of two events.
  29. What is the Addition Law equation?
  30. Which counting rule do you use when the order does NOT matter?
    • Combinations
    • NOT permutations
  31. Rolling a die
    A = {3,4,5,6}
    B = (2,3,4}
    What is  ?
    What is  ?
    •  {3, 4}
    •  {2,3,4,5,6}
  32. If rolling a die and  {3,4}, what is  ?
    2/6 or 1/3
  33. If rolling a die and  {2,3,4,5,6}, what is P ?
    5/6
  34. What are mutually exclusive events?
    • Have no sample points in common
    • If one occurs, the other cannot occur
  35. What is true if Events A and B are mutually exclusive?
  36. What is the Addition Law equation of Events A and B if Events A and B are mutually exclusive?



  37. Are X and Y mutually exclusive?
    • No -  would be 0
  38. What is Conditional Probability?
    • The probability of an event A, given that the event B has occurred
  39. What is the Conditional Probability equation?
  40. What happens to the sample space in  ?
    Event A is restricted to the new sample space of B
  41. P(A) = 2/3
    P(B) = 1/2

    What is  ?
    • 2/3



  42. What is P(B|A)?
    • 1/2
  43. A = {3,4,5,6}
    B = {2,3,4}
     {3,4}
    What is P(A)?
    What is P(B)?
    What is  ?
    • P(A) = 2/3
    • P(B) = 1/2
    • 1/3
  44. C = {1,2}
    A = {3,4,5,6}
    Are Events A and C mutually exclusive?
    • Yes
  45. What is the Multiplication Rule used for?
    Compute the intersection between 2 events
  46. What is the equation for the Multiplication Rule?




  47. What is P(B)?
    • 0.82


  48. What is ?
    • 0.16

  49. Given a standard deck of cads, what is the probability of drawing a red card, given that it is a face card?
    • 0.5



  50. Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?
    • 0.24

  51. If P(A) is not changed or affected by the existence of event B, then A and B are what?
    Independent events
  52. P(A|B) = P(A)
    Are A and B independent events?
    Yes
  53. P(A|B) = P(B)
    Are A and B independent events?
    • No
    • P(B|A) = P(B) - This would be independent
  54. A = {3,4,5,6}
    B = {2,3,4}
    Determine if A and B independent using the Conditional Probability method.
    • Independent
    • P(A) = 2/3
    • P(B) = 1/2
    • P(A|B) = 2/3 = P(A)
    • P(B|A) = 1/2 = P(B)
  55. A = {3,4,5,6}
    B = {2,3,4}
    Determine if A and B are independent using the Multiplication rule.
    • Yes
    • P(A) = 2/3
    • P(B) = 1/2
  56. A and B are independent
    P(A) = 0.2
    P(B) = 0.7
    What is
    • 0.14
  57. A and B are independent
    P(A) = 0.2
    P(B) = 0.7
    What is
    • 0.86
  58. A and B are mutually exclusive
    What is
  59. P(A) = 0.3
    P(B) = 0.5

    Are A and B independent?
    • Yes
    • - If independent
  60. P(A) = 0.3
    P(B) = 0.5

    Are A and B mutually exclusive?
    • No
    • - If mutually exclusive
  61. X and Y are mutually exclusive events
    P(X) = 0.30
    P(Y) = 0.35
    What is P(X|Y)?
    • 0
    • - If mutually exclusive
  62. In a probability matrix, what does the bottom right corner contain?
    1.00 meaning 100%

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