Venn Diagram Problem...URGENT. Need answer b4 Monday. Thanx =)?

60 people responded to a movie survey. The following info was obtained:

6 people like comedies, dramas, and sci-fi

13 like comedies & dramas

10 like comedies & sci-fi

11 like dramas & sci-fi

26 like comedies

21 like dramas

25 like sci-fi

Use a Venn Diagram to determine how many of those surveyed liked none of these categories of movies and how many liked ONLY comedies.

PLEASE HELP ME!! This is due on Monday and no matter how many ways I try this problem, the #'s do NOT add up to 60. ONLY 60 people were surveyed. I need SERIOUS HELP!! Thank you guys so much to everyone that answers this! =) It's GREATLY appreciated.

6 Answers

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  • 1 decade ago
    Favorite Answer

    It's easiest to draw a picture for this, but since I can't, I'll do my best to write a description. Imagine three overlapping circles. You are given that 6 people like all three, so in the portion where all three overlap, you have 6.

    Now, 13 people like comedies and drama, but it doesn't say JUST comedies and drama, so you include those people that are already in the middle section since they all like comedies and drama. So, 13-6=7 people JUST like comedies and drama and so 7 goes in that section. Using the same reasoning for comedies and sci-fi, 10-6=4 people JUST like comedies and sci-fi and again for dramas and sci-fi, 11-6=5 JUST like drama and sci-fi.

    26 like comedies, but again, not JUST comedies. You already have that the people who like comedies and drama (7) like comedies, the people that like all three (6) like comedies and the people that like comedies and sci-fi(4) like comedies. So, 26-7-6-4=9. 9 people like JUST comedies.

    Same reasoning for dramas: 21-7-6-5=3 JUST like dramas, and again for sci-fi: 25-4-6-5=10 JUST like sci-fi.

    So in conclusion:

    ONLY comedies: 9

    ONLY drama: 3

    ONLY sci-fi: 10

    ONLY comedy and drama: 7

    ONLY drama and sci-fi: 5

    ONLY sci-fi and comedy: 4

    ALL three: 6.

    Add each of these numbers up and you get 44. 60 people total were surveyed, so 60-44=16 of those surveyed liked none of these categories of movies.

  • 1 decade ago

    Denotes C: Comedies D:Dramas S:Sci-Fi N:None

    # of C and D and S = 6

    # of C and D = 13 => # of C and D and not like S = 13-6 = 7

    # of C and S = 10 => # of C and S and not like D = 10-6 = 4

    # of D and S = 11 => # of D and S and not like C = 11-6 = 5

    # of C = 26 => # of C and not like D&S = 26 - (7 + 6 + 4) = 9

    # of D = 21 => # of D and not like C&S = 21 - (7 + 6 + 5) = 3

    # of S = 25 => # of S and not like C&D = 25 - (4 + 6 + 5) = 10

    # of N = 60 - (9+7+3+4+6+5+10) = 60 - 44 = 16

    9 C 7 D 3

    4 6 5 N 16

    S

    10

  • 1 decade ago

    1) How many surveyed liked NONE of these categories = 60-44= 16 people liked none of these categoies.

    2) How many only liked comedies = 9 people only liked comedy.

    I drew out my own Venn Diagram but I don't know how I'm going to show you it, I could email it.

  • 1 decade ago

    you have comedies, dramas and sci-fi movies. The means three circles in your diagram.

    in the overlaps you'll have people who like: comedies and dramas, comedies and sci-fi, dramas and sci-fi and the one in the middle is for the ones who like all of the movies.

    put 13 in the drama &comedies, 10 in comedies & sci-fi, 11 in dramas &sci-fi. put the left overs in thier proper circles and it should add uo to 60.

    Hope this helps!! :-)

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  • 1 decade ago

    11-6 = 5 who likes sci and dra only

    10-6 = 4 who likes sci and com only

    13-6 = 7 who likes dra and com only

    25-5-4-6=10 who likes sci only

    21-5-6-7=3 who likes dra only

    26-4-6-7=9 who likes com only

    60-10-5-6-4-3-7-9=16 who likes none of these categories.

  • 1 decade ago

    i cant answer it too. there might be something wrong with the problem.

    Source(s): n
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