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.