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11.6 Probabilities Involving OR and NOT
 

11.6 Probabilities Involving OR and NOT

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    11.6 Probabilities Involving OR and NOT 11.6 Probabilities Involving OR and NOT Presentation Transcript

    • 11.6 Probabilities Involving NOT and OR
    • Problem 1
      Imagine throwing a die. What is the probability of getting a 2?
      What is the probability of not getting a 2?
    • Probability of an Event NOT occurring (a.k.a. P (NOT) )
      The probability that an event E will not occur is equal to 1 minus the probability that it will occur
      P (not E) = 1 – P (E)
    • Sample Problems (# 2)
      If you throw a die, what is the probability of not getting an even number?
      If you are dealt one card from a standard 52-deck card, what is the probability of not getting
      A king?
      A heart?
      A picture card?
    • Problem # 3
      Assume that it is equally probable that the pointer will land on any one of the five numbered spaces.
      Find the probability of not getting a 2
      Find the probability of not getting an odd number
    • ODDS
      Odds in favor of an event = P (E)
      P (not E)
      Odds against E = P (not E)
      P (E)
      Note: Odds in favor and odds against are reciprocals.
    • Sample Problems (#4)
      In a standard 52-deck card,
      Find the odds in favor of getting a king
      Find the odds against getting a diamond
      Find the odds in favor of getting a black ace
      Find the odds against getting a red picture card
    • Sample Problems (# 5)
      If you toss 2 coins together, the possible outcomes are {HH, HT, TH, TT}
      Find the odds in favor of getting two heads
      Find the odds against getting a head and a tail.
    • Odds to Probability
      If the odds in favor of event E are a to b, then the probability of the event is
      P(E) = a
      a + b
      Example: The odds in favor of winning a horse winning a race are 2 to 5. What is the probability that the horse will win?
    • Probabilities Involving OR
      Mutually exclusive events – events that occur simultaneously
      If A and B are mutually exclusive events, then
      P(A or B) = P (A) + P(B)
      Example: In a standard 52-deck card, what is the probability of getting a king or a queen?
    • Sample Problems (# 6)
      If you roll a single die, what is the probability of getting:
      3 or a 5
      A number less than 3 or number greater than 4
    • Probabilities Involving OR
      What if the events are not mutually exclusive?
      OR Probabilities with events that are not mutually exclusive
      If A and B are not mutually exclusive, then
      P(A or B) = P(A) + P(B) – P (A and B)
      Suppose you’re asked to pick a card from a standard 52-deck card. What is the probability of getting a king or a diamond?
    • Sample Problems (# 7)
      Assume that it is equally probable that the pointer will land on any one of the five numbered spaces.
      What is the probability of getting a number greater than 2 or an odd number?
      What is the probability of getting an odd number or a number less than or equal to 3?
    • Assignment
      Class work: pages 601-602, #s 5, 9, 15, 23, 33
      HW: pages 601-603, #s 2-66 (even)