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Math Help - Probability and Venn Diagrams

  1. #1
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    Question Probability and Venn Diagrams

    Hello,

    I am struggling through a math problem dealing with probability and Venn Diagrams and I am at my whits end at this point. It is just not working out for me.

    A development has 425 new homes for sale. 113 of the homes are green, 315 have a porch, 60 have a garage, 45 are green and have a porch, 23 are green and have a garage, 41 have a porch and a garage, and 12 are green and have a have a porch and have a garage.

    a. How many homes are not green, do not have a porch, and do not have a garage?
    In this instance, I tried to put everything into a Venn Diagram to find out where my numbers lie and then subtracted the total in the diagramed circles from the universal set of 425 new homes. I came up with a total of 34 homes.

    b. How many homes are not green, but have a porch and a garage?
    In this instance, I looked at how many total homes that have both a garage and a porch, but are not green (241+29) and got 270.

    I am having problems with the figures to be sure that I accounted for everything correctly:
    Green (but no porch or garage)= 57
    Green and a garage= 11
    Green and a porch= 33
    Green, and porch, and garage=12
    Garage and porch= 29
    Garage (but no porch and not green)= 8
    Porch (but no garage and not green)= 241
    None of these= 34


    Can you please look this over to see if I am heading in the right direction or if I am still as lost as ever? I thank you for any guidance or assistance that you can provide.
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  2. #2
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    Re: Probability and Venn Diagrams

    Hello, tizpan!

    A development has 425 new homes for sale.
    . . 113 of the homes are green,
    . . 315 have a porch,
    . . 60 have a garage,
    . . 45 are green and have a porch,
    . . 23 are green and have a garage,
    . . 41 have a porch and a garage,
    . . 12 are green and have a have a porch and have a garage.

    (a) How many homes are not green, do not have a porch, and do not have a garage?

    I tried to put everything into a Venn Diagram to find out where my numbers lie,
    then subtracted the total in the circles from the universal set of 425 new homes.
    I came up with a total of 34 homes. . Right!


    (b) How many homes are not green, but have a porch and a garage?

    I looked at how many total homes that have both a garage and a porch,
    . . but are not green (241+29) and got 270. . No

    I am having problems with the figures to be sure that I accounted for everything correctly:

    Green (no porch, no garage) = 57
    Green and garage (no porch) = 11
    Green and porch (no garage_ = 33
    Green, and porch, and garage =12
    Garage and porch (not green) = 29 .← This is the answer to (b).
    Garage (no porch, not green) = 8
    Porch (no garage, not green) = 241
    None of these = 34

    From this list, I assume your Venn diagram is correct.
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  3. #3
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    Re: Probability and Venn Diagrams

    Ahhhh, that's is where I went wrong! There were so many variables in there that they all started to sound the same and I was getting confused. It is good to know that I was heading in the right direction, I just couldn't see the answer in front of my face!! Thank you, Soroban, your help is greatly appreciated.
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  4. #4
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    Jaipur,Rajasthan
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    Re: Probability and Venn Diagrams

    Its my favorite subject all time.
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