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Homework Help: Statistics Problem - Venn Diagrams

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data
    The entering class in an engineering college has 34% who intend to major in mechanical engineering, 33% who indicate an interest in taking advanced math as part of their major field of study, and 28% who intend to major in electrical engineering, while 23% have other interests. In addition, 59% are known to major in mechanical engineering or take advanced mathematics. Assuming that a student can major in only one field, what percent of the class intends to major in mechanical engineering or in electrical engineering, but shows no interest in advanced mathematics?


    2. Relevant equations
    This is obviously a Venn diagram-esque problem, but the wording is extremely difficult to comprehend!


    3. The attempt at a solution

    I started drawing a three-circle Venn Diagram, attempting to add in the percentages in the correct areas. The 23% who have other plans lies outside the Venn diagram. However, it doesn't seem to make sense. Can anyone attempt to clarify this problem up for me as well as give me a helpful hint to push me in the right direction? I appreciate all help in advance! Thank you much!
     
  2. jcsd
  3. Jun 8, 2010 #2
    Hmmm. I don't like the wording either. Maybe someone else can chime in here, but I am interpreting the problem as:

    If we let:

    ME = {mechanical engineers}
    AM = {advanced math people}
    EE = {elec engineers}
    O = {others}

    Then I am interpreting the given information as

    ME = .34
    AM = .33
    EE = .28
    O = .23
    EE = .28

    I believe that ME and AM are not mutually exclusive (that is, belonging to one does not exclude you from belonging to the other).

    We are also given:
    (ME ⋃ AM) = .59

    And we are asked to find:
    ((ME ⋃ EE) - AM)

    That is how I would interpret it. Maybe someone else could confirm?
     
  4. Jun 9, 2010 #3
    Yes, that is how I ended up working it out as well. How I ended up solving was sort of using a variation of the addition theorem:

    = P(M or E) and (1 - P(M and A)*P(E and A)) = 0.62 * (1 - 0.59 * 0.51) = .4334

    That seems like a reasonable answer to me. If you don't think this is the correct method, please let me know. Thanks again for the help!
     
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