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Math Help - Percentage help

  1. #1
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    Percentage help

    In a certain town, three newspapers are published. 20% read A, 16% percent read B, 14% read C. 8% read both A and B, 5% of the read both A and C, 4% read both B and C and 2% read all 3 newspapers.

    What percentage of the population read
    a) none of the papers b) at least one of the papers c)exactly one of the papers d) either A or B e) A only?

    Please tell me the answers to these 5 questions and show me a method to do it

    thanks
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  2. #2
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    Venn diagram

    Hello Sulaiman

    Welcome to Math Help Forum!
    Quote Originally Posted by Sulaiman View Post
    In a certain town, three newspapers are published. 20% read A, 16% percent read B, 14% read C. 8% read both A and B, 5% of the read both A and C, 4% read both B and C and 2% read all 3 newspapers.

    What percentage of the population read
    a) none of the papers b) at least one of the papers c)exactly one of the papers d) either A or B e) A only?

    Please tell me the answers to these 5 questions and show me a method to do it

    thanks
    You need to use what's called a Venn diagram - see the attachment below.

    I've completed all the regions of the diagram for you. I started in the centre, where all three loops overlap, writing in 2% for the numbers who read all three newspapers.

    Then I worked outwards, filling in the 6%, 2% and 3%, bearing in mind that we've already located 2% in the centre, thus subtracting this 2% from the figures that are given who read two newspapers.

    Then, again by subtraction, I filled in the 9%, 6% and 7%; and finally, by subtracting the total so far found from 100%, I filled in the 65% who don't read any of these.

    So there's your answer to (a): 65%. Can you work out how to complete the remainder of the questions?

    Grandad
    Attached Thumbnails Attached Thumbnails Percentage help-untitled.jpg  
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  3. #3
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    Thanks a lot I got it now

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  4. #4
    bgn
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    Re: Percentage help

    Quote Originally Posted by Sulaiman View Post
    In a certain town, three newspapers are published. 20% read A, 16% percent read B, 14% read C. 8% read both A and B, 5% of the read both A and C, 4% read both B and C and 2% read all 3 newspapers.

    What percentage of the population read
    a) none of the papers b) at least one of the papers c)exactly one of the papers d) either A or B e) A only?

    Please tell me the answers to these 5 questions and show me a method to do it

    thanks
    Let's try to complete the rest of b), c), d) and e):

    b) In fact, we have got b) done with the answer a); "at least one of the papers" is the supplementary of a), i.e. 1 - 0.65 = 0.35 = 7/20.
    c) Referring to the Vann diagram, "exactly one of the papers" is the sum of the 3 parts on A, B and C which have no any intersections with other events (such that reading 2 or more newspapers). Then the answer is:
    0.09 + 0.06 + 0.07 = 0.22 = 11/50
    d) "Either A or B" means the union of all subparts intersected with A and B, then
    0.09 + 0.06 + 0.06 + 0.02 + 0.03 + 0.02 = 0.28 = 7/25
    e) The original question asks "Find the probability of reading A, given that the person read at least one paper", which tells us that it is a conditional probability:
    P(A|read at least one paper) = P(A^read at least one paper/read at least one paper) = 0.2/0.35 = 4/7.
    f) The original question also asks "Find the probability of reading C, given that the person read either A or B, or both", which tells us that it is the other conditional probability:
    (A|read A, or B or both) = P(C^read A, or B or both/read A, or B or both) = (0.03+0.02+0.02)/(0.09+0.06+0.06+0.03+0.02+0.02) = 0.07/0.28 = 1/4.

    Hope these will help you.

    BGN - Wu
    Last edited by bgn; April 22nd 2014 at 05:48 AM. Reason: have not completed - mispushed the button
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  5. #5
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    Re: Percentage help

    are you really expecting a dialog with the poster of this 4.5 yr old thread?
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