Results 1 to 5 of 5

Math Help - Simple Word Problem Sets, Venn

  1. #1
    Newbie
    Joined
    Jan 2007
    Posts
    5

    Simple Word Problem Sets, Venn

    I'm sure this is a super easy problem, but I've been out of school for five years and didn't take much math my first time since I received a B.A. So I just need a little help getting a jumpstart back into it. I've worked this problem over and over just can't get it to go. Thanks for your help.

    Assume that 170 surveys are completed. Of those surveyed, 88 responded positively to effectiveness, 93 responded positively to side effects, and 80 responded positively to cost. Also, 47 responded positively to both effectiveness and side effects, 37 to effectiveness and cost, 47 to side effects and cost, and 20 to none of the items. How many responded to all three?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Tainted1 View Post
    I'm sure this is a super easy problem, but I've been out of school for five years and didn't take much math my first time since I received a B.A. So I just need a little help getting a jumpstart back into it. I've worked this problem over and over just can't get it to go. Thanks for your help.

    Assume that 170 surveys are completed. Of those surveyed, 88 responded positively to effectiveness, 93 responded positively to side effects, and 80 responded positively to cost. Also, 47 responded positively to both effectiveness and side effects, 37 to effectiveness and cost, 47 to side effects and cost, and 20 to none of the items. How many responded to all three?

    150 surveys had some response.

    Of these:

    150-88-93-80+47+37+47=20

    responded to all three (this is an example of the inclusion/exclusion principle)

    We start with the number of surveys with response subtract the numbers
    of repsonses to each question, but now we have removed those that
    responded to more than one question multiple times - twice for those that
    answered exactly two questions and three times for those that responded
    to all three.

    So adding back in the numbers that responded to each pair of questions
    we have removed those who answered exactly two questions, and left
    one count in for each person who responded to all three.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Here's the diagram.

    170-88-93-80+47+47+37-20=20
    Last edited by galactus; November 24th 2008 at 05:39 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,749
    Thanks
    650
    Hello, Tainted1!

    No, this is not an easy problem . . . even with Venn diagrams.


    170 surveys are completed. .Of those surveyed, their positive responses were:

    88 to Effectiveness
    93 to Side effects
    80 to Cost

    47 to Effectiveness and Side effects
    37 to Effectiveness and Cost
    47 to Side effects and Cost

    20 to none of the items.

    How many responded to all three?
    There is a formula for the number of elements in the union of three sets.

    n(E \cup S \cup C) \;=\;n(E) + n(S) + n(C) - n(E\cap S) - n(S\cap C)  - n(E\cap C) + n(E \cap S \cap C)


    Of the 170 surveys, 20 responded to none of the three.
    . . Then there are 150 who responded to at least one.

    The formula becomes: . 150 \:=\:88 + 93 + 80 - 47 - 37 - 47 + n(E \cap S \cap C)

    Therefore: . n(E \cap S \cap C) \:=\:20

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2007
    Posts
    5

    Thumbs up Thank You

    Thank you everyone. It is much clearer now. Math isn't my best subject so I'm sure I'll be back.

    Thanks again.

    T
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Venn Diagram and sets
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 21st 2010, 06:13 AM
  2. Help with venn diagrams/sets word problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 21st 2010, 04:04 AM
  3. Sets and Venn Diagram problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 18th 2008, 06:14 AM
  4. use venn diagram to figure out word problem?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 25th 2008, 11:48 AM
  5. Replies: 2
    Last Post: February 20th 2008, 10:14 AM

Search Tags


/mathhelpforum @mathhelpforum