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Introductory Statistics: Conditional Probability and Multiplication Rules

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Termini in questo insieme (20)

  • What is conditional probability?
    Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(F|E).
  • How do you calculate the probability of two dependent events both occurring?
    Use the general multiplication rule: P(E and F) = P(E) · P(F|E).
  • What is the multiplication rule for independent events?
    For independent events E and F, P(E and F) = P(E) · P(F).
  • What is the difference between independent and dependent events?
    Events are independent if the occurrence of one does not affect the probability of the other; dependent if it does.
  • What does it mean if two events are disjoint?
    Disjoint events have no outcomes in common; if one occurs, the other cannot.
  • Are disjoint events independent?
    No, disjoint events are not independent because knowing one occurs changes the probability of the other to zero.
  • What is the complement rule in probability?
    The complement of event E, denoted Ec, is the event that E does not occur, and P(E) + P(Ec) = 1.
  • How do you calculate the probability of 'at least one' event occurring?
    Use the complement rule: P(at least one) = 1 - P(none).
  • What is the probability that a randomly selected person is a man from the given table?
    P(man) = (Number of men) / (Total people) = (1+2) / (1+7+2+3) = 3/13.
  • What is the probability that a randomly selected person is a male doctor from the table?
    P(male doctor) = Number of male doctors / Total people = 2 / 13.
  • How do you find the probability that a person is a nurse or a doctor?
    Add the probabilities of nurses and doctors: P(nurse or doctor) = (1+7+2+3)/13 = 13/13 = 1.
  • How do you find the probability that a person is a nurse or a woman?
    Add probabilities of nurses and women, subtract overlap: P(nurse or woman) = P(nurse) + P(woman) - P(nurse and woman).
  • What is the probability that a person who is a nurse is a man?
    P(man | nurse) = Number of male nurses / Total nurses = 1 / (1+7) = 1/8.
  • What is the probability that a person is a doctor given that the person is a woman?
    P(doctor | woman) = Number of female doctors / Total women = 3 / (7+3) = 3/10.
  • What is the probability that a person is a woman given that the person is a doctor?
    P(woman | doctor) = Number of female doctors / Total doctors = 3 / (2+3) = 3/5.
  • What is the range of any probability value?
    The probability of any event must be between 0 and 1 inclusive: 0 ≤ P(E) ≤ 1.
  • What must the sum of probabilities in a sample space equal?
    The sum of probabilities of all outcomes in the sample space must equal 1.
  • What is the formula for the probability of the union of two events E and F if they are not disjoint?
    P(E or F) = P(E) + P(F) - P(E and F).
  • What is the formula for the probability of the union of two disjoint events E and F?
    If E and F are disjoint, then P(E or F) = P(E) + P(F).
  • What is the 5% guideline for assuming independence in sampling?
    If the sample size is no more than 5% of the population, treat selections as independent even if sampling without replacement.