Math 219: Section 5.2-5.4

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lazvertiigo
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285387
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Math 219: Section 5.2-5.4
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2014-10-10 19:16:40
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Addition Rule Disjoint Events General Complement Multiplication
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Math 219 Statistics and Probability, SCC, Stewart III
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  1. Two event are _______ if they do not have any outcomes in common.
    disjoint
  2. Another name for disjoint event is _______events.
    mutually exclusive
  3. What kind of diagram is this?
    Venn Diagram

  4. The entire rectangle represents the _______ and each circle represents an _______.
    Sample Space, Event
  5. What is the formula for the Addition Rule for Disjoint Events?
    P(E or F) = P(E) + P(F)
  6. T/F:  If E and F are disjoint (mutually exclusive) events, then 
    P(E or F) = P(E)P(F)
    • False.
    • P(E or F) = P(E) + P(F)
  7. T/F: The Addition Rule for Disjoint Events can be extended to more than two disjoint events.In general, if E, F, G, . . . each have no outcomes in common (they are pairwise disjoint), then
    P(E or F or G or ...) = P(E) + P(F) + P(G) +...
    True
  8. T/F: The addition rule only applies to events that are disjoint.
    True
  9. What is the formula for The General Addition Rule?
    P(E or F) = P(E) + P(F) - P(E and F)
  10. If two events are not disjoint, then this idea must be modified because some outcomes will be double counted.  This is called...
    The General Addition Rule
  11. What is The Complement Rule formula?
    P(Ec) = 1 - P(E)
  12. T/F:  The Complement rule states--If E represents any event and Ec represents the complement of E, where the complement consists of all the outcomes that are not in event E, then
    P(Ec) = 1 - P(E)
    True
  13. T/F: The Addition Rule shows how to compute “and” probabilities, P(E and F), under certain conditions.
    • False.
    • The Addition Rule shows how to compute “or” probabilities, P(E or F), under certain conditions.
  14. Two events are ________ if the occurrence in one event does not affect the probability of the second event.
    independent
  15. Two events are ________ if the occurrence in one events does affect the probability of the second event.
    dependent
  16. What’s the difference between disjoint events and independent events?
    Disjoint events can never be independent. Consider two events E and F that are disjoint. We know if event E occurred, then we know F did not occur.

    Independent events implies that event E does not affect the probability of event F. Therefore, knowing two events are disjoint means that the events are not independent
  17. T/F:  Disjoint events can never be dependent.
    • False:
    • Disjoint events can never be independent.

    Consider two events E and F that are disjoint. We know if event E occurred, then we know F did not occur.
  18. T/F:
    Independent events implies that event E does not affect the probability of event F.
    True.
  19. T/F: knowing two events are disjoint means that the events are dependent.
    • False.
    • knowing two events are disjoint means that the events are not independent.
  20. What is the formula for the Multiplication Rule?
    P(E and F) = P(E)P(F)

    E and F are independent events.
  21. T/F:
    We can extend the Multiplication Rule for only three independent events.
    • False.
    • We can extend the Multiplication Rule for three or more independent events.
  22. What is the Multiplication Rule for n independent Events?
    If events E1, E2,...,En are independent, then

    P(E1 and E2 and E3 and ... and En)=P(E1)P(E2)P(E3)...P(En)
  23. What is the formula of the "at least" probability?
    P(at least one) = 1 - P(none)
  24. T/F:
    If E and F are disjoint events, then P(E or F) = P(E) + P(F) – P(E and F). If E and F are not disjoint events, then P(E or F) = P(E) + P(F).
    • False.
    • If E and F are disjoint events, then P(E or F) = P(E) + P(F). If E and F are not disjoint events, then P(E or F) = P(E) + P(F) – P(E and F).
  25. T/F:
    If E and F are independent events, then P(E and F) = P(E)∙P(F)
    True.
  26. What is the term that defines: The notation P(F|E) is read “the probability of event F given event E.” It is the probability that an event F occurs, given E has occurred.
    Conditional Probability
  27. What is the Conditional Probability Rule?
    If E and F are any two events, then

    P(FE) = P(E and F) / P(E)
  28. What term defines:
    The probability that two events E and F both occur is
    P(E and F) = P(E)P(E|F)
    General Multiplication Rule
  29. Two events E and F are independent if P(E|F)=P(E) or, equivalently, if ____________.
    P(F|E) = P(F)
  30. T/F:
    The classical method, when all outcomes are equally likely, involves counting the number of ways things can occur.
    True.
  31. What defines a task that consists of a sequence of choices with p selections for the first choice, q selections for the second choice, r selection for the third choice, and so on, then the number of different tasks is p∙q∙r∙∙∙?
    The Multiplication Rule of Counting
  32. What defines the following: If n ≥ 1 is an integer, n! = n(n-1)(n-2)...(2)(1)?
    the factorial symbol
  33. What term defines an ordered arrangement in which r different objects are chosen out of n different objects and repetition is not allowed?
    A permutation:  nPr
  34. What is the formula for Permutations?
    nPr = n! / (n-r)!
  35. What are the three conditions for Permutations?
    • 1. the n objects are distinct
    • 2. repetition of objects is not allowed
    • 3. order of arrangement matters
  36. T/F:
    Repetition of objects is allowed for Permutations.
    • False.
    • Repetition of objects is not allowed for Permutations.
  37. T/F:
    The order of choice does not matter in combinations.
    True.
  38. What term defines a collection, without regards to order, of n different objects without repetition for r different objects chosen.
    Combinations, nCr
  39. What is the formula for Combinations?
    nCr =n! \ [r!(n-1)!]
  40. What are the conditions for the use of Combinations?
    • 1. the n objects are distinct
    • 2. repetition of objects is not allowed
    • 3. order does not matter
  41. What formula do you use for Permutations with Non-distinct Items?
    n! \ (n1!n2!n3!...nk!)
  42. What defines the following: The number of permutation of n objects where there are n1 of the first kind, n2 objects of the second kind,…, and nk objects of the kth kind.
    Permutations with Non-distinct Items
  43. Probabilities using the _____________involve counting the number of possibilities and often the number of possibilities is some permutation or some combination.
    classical method
  44. T/F:
    The permutation and combination formula can be used to calculate probabilities.
    True.
  45. What type of Counting Technique would you use for the following:  
    In a horse racing “Trifecta”, a gambler must pick which horse comes in first, second, and third. If there are 8 horses in the race, and every order of finish is equally likely, what is the chance that any ticket is a winning ticket?
    • Permutations.
    • The 8 horses are distinct, no repetition is allowed, and the order matters.
  46. What type of counting technique would you use for the following: 
    The Powerball lottery consists of choosing 5 numbers out of 55 and then 1 out of 42. The grand prize is given when all 6 numbers are correct. What is the chance of getting the grand prize?
    • Combinations.
    • Each number is distinct; there is no repetition, and the order of the numbers does not matter as long as they match.
  47. What type of counting technique would you use for the following:
    If there are eight researchers and three of them are to be chosen to go to a meeting, then how many ways can we choose three researchers?
    • Combinations.
    • The 8 researchers are distinct; repetition is not allowed, and the order in which the individuals are selected do not matter.
  48. What type of counting technique would you use for the following:
    In how many ways can people in a 1000-person marathon finish first, second, and third?
    • Permutations.
    • The 1000 people are distinct, a person cannot repeatedly cross the finish line, and the order of finishing the race matters.
  49. What type of counting technique would you use for the following:
    Let’s say the child is coloring a picture of a shirt and pants, but now the child wants to use two different colors out of five distinct colors. How many ways can this be colored?
    • The Multiplication Rule of Counting
    • or Permutations (5 distinct colors, repetition is not allowed, and order matters)
  50. What type of counting technique will you use for the following: 
    A child is coloring a picture of shirt and pants. If there are five different colors of markers, then how many ways can the shirt and pants be colored?
    • The Multiplication Rule of Counting
    • Repetition is allowed since it is not specifically stated.

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