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Math Help - Beginner probability question

  1. #1
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    Beginner probability question

    At the start of flue season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a headache, 24 have a cold, and 12 have neither symptoms. Some patients have both symptoms.

    Draw a Venn diagram and determine the number of patients that have both symptoms.

    How do I figure out how many have both?

    The answer is this (8a):
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  2. #2
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    Is the question \|A\cap B\|=~?

    If so the give tells you that \|\overline{A\cup B}\|=12 (complement).

    So 38=\|A\cup B\|=\|A\|+\|B\|-\|A\cap B\|.
    Last edited by Plato; April 9th 2011 at 11:34 AM.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Is the question \|A\cap B\|=~?
    Yes I believe that's what it's asking for.

    Quote Originally Posted by Plato View Post
    If so the give tells you that \|\overline{A\cup B}\|=12 (complement).

    So 48=\|A\cup B\|=\|A\|+\|B\|-\|A\cap B\|.
    I'm assuming you meant 38 (50-12):

    38 = \displaystyle \frac{30}{50} + \displaystyle \frac{24}{50} - \|A\cap B\|

    I can tell that looks completely wrong. Have I misunderstood something?
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  4. #4
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    Quote Originally Posted by IanCarney View Post
    38 = \displaystyle \frac{30}{50} + \displaystyle \frac{24}{50} - \|A\cap B\|

    I can tell that looks completely wrong. Have I misunderstood something?
    It should be 38 = 30 + 24 - \|A\cap B\|.
    So \|A\cap B\|=30+24-38=16 just as in the diagram.
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