Thread: Application of Venn Diagrams

Hello, all. So, I've been sitting here for at least an hour attempting to figure this out, but no dice.

A recent transportation survey of w urban commuters (that is, n(U)=w) yielded the following information:

X rode neither trains nor buses

Y rode trains
Z rode only trains

How many people rode (a) trains and buses, (b) only buses, (c) buses, and (d) trains or buses?

Basically what I got to was:




I really have no idea where X would go. Not sure if I would add it to W for some reason or if I would just exclude it. I also figured that Y could go within the intersection, but I was not exactly sure of this. Either way, this is as far as I've gone and it doesn't look like I am able to get much further.

Any input would be greatly appreciated.

Look at the diagram.
x=a, y=b+c, z=b, w=a+b+c+d.

Answers.
(a) c
(b) d
(c) c+d
(d) b+c+d

Thank you. Makes sense. Also, I have another that I think I did correctly, but would like someone to check it, if that isn't too much trouble.

In a recent health insurance survey, employees at a large corporation were asked, "Have you ever been a patient in a hospital during the past year, and if so, for what reason?" The following results were obtained:

494 had an injury
774 had an illness
1254 has tests
238 had and injury and an illness and tests
700 had an illness and tests
501 had tests and no injury or illness
956 had an injury or illness
1543 had not been a patient

(a) What percent of the employees had been a patient in the hospital?
(b) What percent of the employees had tests in the hospital?

And here's what I got:


A {They had an injury}
B {They had an illness}
C {They had tests}

n(U) = 3000

(a) ~48.7% had been a patient
(b) 41.8% had tests performed

So?