Thread: Probability and Venn Diagrams

1. 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.

2. 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.

3. 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.

4. Re: Probability and Venn Diagrams

Its my favorite subject all time.