Question 1164105
<pre>

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"a=?"),
locate(-3.5,-2,"j=?"),
locate(0,-2.7,S),
locate(-.45,-1,"i=?"),
locate(.6,.4,"h=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,B),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,C),
locate(-1.5,.5,"f=?"),
locate(-.4,2.3,"d=?"),
locate(1.8,2,"e=?"),
locate(-.4,1.1,"g=?") )}}}

Begin with n(B∩C∩S)=g=21
Then go to n(B∩S)=f+g=33, and you can get f.
Then go to n(B∩C)=d+g=31, and you can get d.
Then go to n(B)=a+d+f+g=47, and you can get a.
Then go to n[(B∩C)∪(B∩S)∪(C∩S)]=d+g+f+h=51, and you can get h.
Then go to n(C)=d+e+g+h=46, and you can get e.
Then go to n(S)=f+g+h+i=52, and you can get i.
Finally, go to "75 patients", a+d+e+f+g+h+i+j=75, and you can get j.

(a) had high blood pressure or high cholesterol, but not both? 

That's a+f+e+h.


(b) had fewer than two of the conditions listed?

That's a+e+i+j.


(c) were smokers, but did not have high blood pressure or high cholesterol?

That's i.


(d) did not present exactly two of the conditions on the list?

That's a+e+i+g+j

You can fill in the question marks in the Venn diagram, then add
them up to answer the questions.

Edwin</pre>