Help to check my work:
In a survey of 500 people, 200 indicated that they could be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car. How many will purchase neither. How many will purchase only a car?

Question

Help to check my work: 
In a survey of 500 people, 200 indicated that they could be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car. How many will purchase neither. How many will purchase only a car?

anonymous · Answer

$$n(\Omega)$$: Total number of people.

anonymous · Answer

$$n(A)$$: number of people that will buy a major appliance.

anonymous · Answer

$$n(B)$$: number of people that will buy a car.

anonymous · Answer

$$n(C)$$: number of people that will buy both.

anonymous · Answer

$$C = A intersection B$$

anonymous · Answer

So, to get the howmany will purchase a car:

anonymous · Answer

$$n(A\C)=n(A)-n(A\intersection B)$$

anonymous · Answer

So, $$n(A\C)=200 - 25 = 175$$

turingtest · Answer

I'm not sure about the formulas for this kind of thing but I get the same answer.

mertsj · Answer

150 will buy a car.

turingtest · Answer

oh no I don't, I get 125 for the 'neither' part

mertsj · Answer

The problem tells you that.

anonymous · Answer

And to get How many will purchase either:
$$n((A \cup B)^C)=n(\Omega)-n(A\cup B)=n(\Omega) - n(A)-n(B)+n(A intersection B)$$

mertsj · Answer

Draw a Venn Diagram

anonymous · Answer

I haven't calculated yet, but I will use that formula \TuringTest

anonymous · Answer

I did it to get my formulas @Mertsj

turingtest · Answer

why are you adding the intersection in that formula? is that right above?

anonymous · Answer

Because : $$n(A\cup B) = n(A) + n(B) - n(A intersection B)$$

anonymous · Answer

I got 175 for the neither part =(

turingtest · Answer

oh, is it because we counted the people who will buy one or the other in with those who will buy both? then it makes sense

turingtest · Answer

ok then the number of people who will buy JUST a car is not 150

anonymous · Answer

yes, is say, How many will buy only

anonymous · Answer

a car

anonymous · Answer

So, do you think I am right?

mertsj · Answer

125 will buy only a car

anonymous · Answer

Why Mertsj?

anonymous · Answer

What is wrong with my formula?

mertsj · Answer

Because it says that 150 will buy a car and 25 will buy both a car and an appliance.  150-25 = 125

anonymous · Answer

Ahh yes! I made a mistake with the numbers. sorry

anonymous · Answer

but what do you think of the neither part?

turingtest · Answer

It also makes the neither part 150, yes?

anonymous · Answer

I guess I'm over complicating the things

mertsj · Answer

500 -[200+150-25]=500-325=175

anonymous · Answer

No I still get 175

turingtest · Answer

because 200 buy a car and 150 buy an appliance (forget the "both" it doesn't matter)
350 bought something
so
500-350=150 did not

turingtest · Answer

I git the 200 and the 150 backwards, but it is the same idea

mertsj · Answer

Yes you are over complicating things and going around Robin Hood's barn to boot.

anonymous · Answer

But if you forget about the "both" part you're counting twice?

mertsj · Answer

No Turing.  You are counting the 25 who bought both twice.

turingtest · Answer

oh, am I?

anonymous · Answer

What is the meaning of Robin Hood's barn to boot?

mertsj · Answer

175 bought only a MA.  125 bought only a car.  25 bought both.  So 325 bought something.

anonymous · Answer

Yes, I think there is no reason to forget the both part.

turingtest · Answer

oh ok... my bad :(

anonymous · Answer

Anyway, thank you so mucho for the help guys =).

mertsj · Answer

yw