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College Math

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Movies A survey of 350 customers was taken at Regal Cinemas in Austin, Texas, regarding the type of movies customers liked. The following information was determined.
• 196 liked dramas.
• 153 liked comedies.
• 88 liked science fiction.
• 59 liked dramas and comedies.
• 37 liked dramas and science fiction.
• 32 liked comedies and science fiction.
• 21 liked all three types of movies
Of the customers surveyed, how many liked
• a) none of these types of movies?
• b) only dramas?
• c) exactly one of these types of movies?


I do not know how to determne how to get the answers the A, B and C nor how to input it into a Venn Diagram

  • College Math -

    Draw 3 overlapping circles, D, C and SF.

    Way in the middle where all three overlap, put 21

    Where only D and C overlap, put 59

    Where D has no overlap with others pu 196

    etc
    now you have to work from the inside out
    to figure out how many like each 2 or each 1 exclusively
    For example those liking only D and C
    are
    59-21 = 38
    D and SF = 37-21 =16
    C and SF = 32-21 = 11
    then
    those liking D alone = 196 - 38-21-16 =
    121
    those liking C alone = 153-38-21-11 =
    83
    those liking SF alone = 88-16-11-21 =
    40
    NOW do the problem
    a
    none = 350 - 121-38-21-16-83-11-40 = 20
    b
    121
    c
    121+83+40 = 244
    Check my arithmetic!!!

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