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Probability Problems

  1. May 2, 2005 #1
    A viewer preference survey conducted by a cable-television network revealed that 46% of viewers watch sports, 31% watch comedy, and 33% watch drama. Of these viewers, 13% watch sports and comedy, 9% watch comedy and drama, and 11% watch sports and drama. Suppose 20% of viewers watch none of these 3 types of shows. What is the probability that a randomly selected person watches all three?

    I have no idea how to do this problem. I tried using a venn diagram, but that didn't seem to work..

    And for this problem:
    In a card game, a hand of 5 cards contains at least 2 spades. What is the probability that there are exactly 4 spades in that hand?

    I tried doing 5C4(13/52)^4(39/52), but it wasn't correct..
  2. jcsd
  3. May 2, 2005 #2


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    I think you can do the first one with a Venn diagram approach. Draw three circles with mutual overlap and label the 7 separate regions as A,B,C,D,E,F, and G, with G in the middle (see diagram). You are told that the total region is .80, and you are told the area of each circle. The way I drew mine these are

    A + D + E + G = .41
    B + F + E + G = .31
    C + D + F + G = .33

    Add these three

    A + B + C + 2D + 2E + 2F + 3G = .105


    A + B + C + D + E + F + G = .80

    Take the difference.

    D + E + F + 2G = .25

    The rest of the problem involves finding D + G, E + G, and F + G from the information given, and solving for G

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