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anonymous

  • 4 years ago

A group of 1000 patients each diagnosed with a certain disease is being analyzed with regard to the disease symptoms present. The symptoms are labeled A,B,and C, and each patient has at least one symptom. Also, 900 have either symptom A or B (or both) 900 have either symptom A or C (or both) 800 have either symptom B or C (or both) 650 have symptom A 500 have symptom B 550 have symptom C Determine: 1. The number who had both symptoms A and B 2. The number who had either symptom A or B (or both) but not C 3. The number who had all three symptoms I cant seem to figure this out..

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  1. anonymous
    • 4 years ago
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    1. (just A + just B)-(900 have either symptom A or B (or both)= 250

  2. anonymous
    • 4 years ago
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    what does your number 2 mean?

  3. anonymous
    • 4 years ago
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    |dw:1328113317366:dw|

  4. anonymous
    • 4 years ago
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    if you continue this pattern tho, and 500 have B, your already at 500 right? so that leavesno one having all three or just B? That is why I am confused. PLEASE HELP :)

  5. anonymous
    • 4 years ago
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    i'm thinking............

  6. mathmate
    • 4 years ago
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    You can apply the principle of inclusion/exclusion. For 1, \(|A \cup B| = |A|+ |B| - |A \cap B| \) => \(|A \cap B| = |A|+ |B| - |A \cup B| \) =650+500-900=250 Similarly \(|B \cap C| = |B|+ |C| - |B \cup C| \) = 500+550-900=150 and \(|C \cap A| = |C|+ |A| - |C \cup A| \) = 550+650-800=400 For 2, The answer is in the given data. For 3, \(|A \cup B \cup C| = |A|+ |B| + |C| - |A \cap B|- |B \cap C|- |C \cap A| + |A\cap B \cap C| \) which means \(|A \cap B \cap C| = |A \cup B \cup C| - |A|- |B| - |C| + |A \cap B|+ |B \cap C|+ |C \cap A| \) =1000-650-500-550+250+150+400 = 100 For more information, see http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

  7. anonymous
    • 4 years ago
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    omg. i didn't mentioned that all of the patients are 1000

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