12.4 probability of compound events

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12.4 probability of compound events

  1. 1.  The union or intersection of two events iscalled a compound event. Union of A and B: All outcomes foreither A or B Intersection of A and B: Only outcomes sharedby both A and B
  2. 2.  If the intersection of A and B is empty, then Aand B are mutually exclusive events. This means, outcomes for events A and Bnever overlap.
  3. 3.  P(A and B) = probability of outcomes that fallin the intersection P(A or B) = P(A) + P(B) – P(A and B) If A and B are mutually exclusive: P(A or B) = P(A) + P(B)
  4. 4.  A card is randomly selected from a standard52-card deck. What is the probability that itis an ace or a face card?
  5. 5.  You roll a six-sided die. What is theprobability of rolling a multiple of 3 or 5?
  6. 6.  A card is randomly selected from a standarddeck. What is the probability it is a heart orface card?
  7. 7.  You roll a six-sided die. What is theprobability of rolling a multiple of 3 or amultiple of 2?
  8. 8.  Last year a company paid overtime or hiredtemporary help during 9 months. Overtimewas paid in 7 months and temps were hiredin 4. An auditor randomly selects a month tocheck the payroll records. What is theprobability that he selects a month when thecompany paid overtime and hired temps?
  9. 9.  In a poll of high school juniors, 6 out of 15took German and 11 out of 15 took math.Fourteen out of 15 took German or math.What is the probability that a student tookboth German and math?
  10. 10.  In a survey of 200 pet owners, 103 had dogs,88 had cats, 25 had birds, and 18 hadreptiles.1. Nobody had both a cat and bird. What isthe probability that they had a cat or bird?2. 52 owned both a cat and dog. What is theprobability of owning a cat or dog?3. 119 owned a dog or reptile. What is theprobability of owning a dog and reptile?
  11. 11.  The complement of A includes all outcomesnot in A. Written A’. Read “A prime”. Probability of A’: P(A’) = 1- P(A)
  12. 12.  A card is randomly selected from a standarddeck. Find the probability that: the card is not a king. The card is not an ace or jack.
  13. 13.  Four houses in a neighborhood have thesame model of garage door opener. Eachhas 4096 possible codes. What is theprobability that at least two houses have thesame code?
  14. 14.  Seven prizes are being given in a rafflecontest. 157 tickets are sold. After eachprize is called, the winning ticket goes backin the drawing. What is the probability that atleast one of the tickets is drawn twice?

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