Statistics Chapter 4: Probabilities

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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?
    Image Upload 1
  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?
    Image Upload 2
  17. What is the equation for Counting Rules Permutations?
    Image Upload 3
  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
    • Image Upload 4
  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
    • Image Upload 5
  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}
    • Image Upload 6 = {2,3,4,5,6}
    • Image Upload 7
  25. What is the notation for Union of 2 Events?
    • Image Upload 8
    • 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 }
    • Image Upload 9 {3,4}
    • Image Upload 10 2/6
  27. What is the notation for the Intersection of 2 Events?
    • Image Upload 11
    • 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?
    Image Upload 12
  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 Image Upload 13 ?
    What is Image Upload 14 ?
    • Image Upload 15 {3, 4}
    • Image Upload 16 {2,3,4,5,6}
  32. If rolling a die and Image Upload 17 {3,4}, what is Image Upload 18 ?
    2/6 or 1/3
  33. If rolling a die and Image Upload 19 {2,3,4,5,6}, what is PImage Upload 20 ?
    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?
    Image Upload 21
  36. What is the Addition Law equation of Events A and B if Events A and B are mutually exclusive?
    Image Upload 22
  37. Image Upload 23
    Image Upload 24
    Image Upload 25
    Are X and Y mutually exclusive?
    • Image Upload 26
    • Image Upload 27
    • Image Upload 28
    • No - Image Upload 29 would be 0
  38. What is Conditional Probability?
    • The probability of an event A, given that the event B has occurred
    • Image Upload 30
  39. What is the Conditional Probability equation?
    Image Upload 31
  40. What happens to the sample space in Image Upload 32 ?
    Event A is restricted to the new sample space of B
  41. P(A) = 2/3
    P(B) = 1/2
    Image Upload 33
    What is Image Upload 34 ?
    • 2/3
    • Image Upload 35
    • Image Upload 36
  42. Image Upload 37
    Image Upload 38
    Image Upload 39
    What is P(B|A)?
    • 1/2
    • Image Upload 40
    • Image Upload 41
  43. A = {3,4,5,6}
    B = {2,3,4}
    Image Upload 42 {3,4}
    What is P(A)?
    What is P(B)?
    What is Image Upload 43 ?
    • P(A) = 2/3
    • P(B) = 1/2
    • Image Upload 44 1/3
  44. C = {1,2}
    A = {3,4,5,6}
    Are Events A and C mutually exclusive?
    • Yes
    • Image Upload 45
  45. What is the Multiplication Rule used for?
    Compute the intersection between 2 events
  46. What is the equation for the Multiplication Rule?
    • Image Upload 46
    • Image Upload 47
  47. Image Upload 48

    Image Upload 49

    What is P(B)?
    • 0.82
    • Image Upload 50
    • Image Upload 51
    • Image Upload 52
  48. Image Upload 53
    Image Upload 54
    What is Image Upload 55 ?
    • 0.16
    • Image Upload 56

    Image Upload 57
  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
    • Image Upload 58

    Image Upload 59

    Image Upload 60
  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
    • Image Upload 61

    Image Upload 62
  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
    • Image Upload 63
    • P(A) = 2/3
    • P(B) = 1/2
    • Image Upload 64
  56. A and B are independent
    P(A) = 0.2
    P(B) = 0.7
    What is Image Upload 65
    • 0.14
    • Image Upload 66
    • Image Upload 67
  57. A and B are independent
    P(A) = 0.2
    P(B) = 0.7
    What is Image Upload 68
    • 0.86
    • Image Upload 69
    • Image Upload 70
  58. A and B are mutually exclusive
    What is Image Upload 71
    • Image Upload 72
    • Image Upload 73
    • Image Upload 74
    • Image Upload 75
    • Image Upload 76
  59. P(A) = 0.3
    P(B) = 0.5
    Image Upload 77
    Are A and B independent?
    • Yes
    • Image Upload 78 - If independent
    • Image Upload 79
  60. P(A) = 0.3
    P(B) = 0.5
    Image Upload 80
    Are A and B mutually exclusive?
    • No
    • Image Upload 81 - 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
    • Image Upload 82 - If mutually exclusive
    • Image Upload 83
    • Image Upload 84
  62. In a probability matrix, what does the bottom right corner contain?
    1.00 meaning 100%
Author:
honestkyle
ID:
198145
Card Set:
Statistics Chapter 4: Probabilities
Updated:
2013-04-11 16:16:32
Tags:
probability events factorals permutations stats
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Description:
Probability
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