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Counting and Probability: Determine product efficacy

  1. Aug 4, 2009 #1
    Three drugs: A, B and C

    50 subjects reported relief from:

    21 drug a
    21 drug b
    31 drug c

    9 a&b
    14 a&c
    15 b&c

    41 report relief from at least one drug

    Note that some of the subjects who reported results from A might have done so for B and C etc.

    a. How many got relief from none of the drugs?

    I assume I use the difference rule here

    50 - 41 = 9 subjects that didn't report any relief.

    b. How many people got relief from all 3 drugs?

    D[A intersection B intersection C] = 21 + 21 + 31 - 9 - 14 - 15 = 35

    such that 41 - 35 = 6 The number of subjects relieved by all three drugs.

    c. How many subjects got relief from A only?

    I'm kind of unsure about this question.

    D[A - (A intersection B) - (A intersection C)]

    So how do I identify the specific users that have ticked in both a int b and a int c?

    21 - 9 - 14 + 6 = 4

    This is all I can think off.
  2. jcsd
  3. Aug 6, 2009 #2


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    Your answer to c is correct, except the formula should be D[A - (A intersection B) - (A intersection C) + (A intersect. B intersect. C)].
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