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Math Help - Venn diagram

  1. #1
    Newbie
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    May 2007
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    Venn diagram

    can someone please tell me if am doing this question right

    in a set of 35 people, 23 are wearing hats, 25 are wearing gloves and 30 are wearing either hats or gloves.

    how many people are wearing:

    (i) both hat and gloves
    (ii) neither hat or gloves

    i) first i take 23 away from 30 to get 7 gloves and then i take 25 from 30 to get 5 hats next i add them together to get 12 then i take it away from 30 to get the ANSWER of 18 that wear both hats and gloves

    ii) i presume the answer is 5?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, red55!

    In a set of 35 people, 23 are wearing hats, 25 are wearing gloves
    and 30 are wearing either hats or gloves.

    How many people are wearing:
    . . (i) both hat and gloves
    . . (ii) neither hat or gloves

    i) First I take 23 away from 30 to get 7 gloves (only),
    and then i take 25 from 30 to get 5 hats (only).
    Next I add them together to get 12,
    then I take it away from 30 to get the ANSWER of 18 . . . . Right!

    I assume you constructed the Venn diagram
    . . or you could have used this formula:

    . . n(H U G) .= .n(H) + n(G) - n(H ∩ G)
    . . . . . . - . - . . . . . . . . . . . . .
    . . . . 30 . . .= . .23 .+ -25 .- .n(H ∩ G)


    Therefore: .n(H ∩ G) .= .23 + 25 - 30 .= .18



    ii) i presume the answer is 5? . . . . Yes!
    Good work!

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