Question 1143506
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            Your formulation is not accurate.

            To be accurate (and to become a true Math problem),  it has to be re-written and re-edited.

            My editing is this:


<pre>
            In a survey concerning the smoking habits of consumer it was found that 
            55% smoke cigarette A, 50% smoke cigarette B,40% smoke cigarette C, 
            30% smoke cigarettes A and B, 20% smoke cigarettes A and C, 12% smoke cigarettes B and C,
            while only 10% smoke all three types of cigarettes. What percentage of the population did not smoke? 
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution is below.



<pre>
The percentage of those who smoke at least one of the three types of cigarettes is


    55 + 50 + 40 - 30 - 20 - 12 + 10 = 93  percents.      (*)


Therefore, 7% of the population do not smoke.      <U>ANSWER</U>
</pre>


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The key to the solution is this alternate sum in the left side of (*).


For this formula, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Challenging-problems-on-counting-elements-in-subsets-of-a-given-finite-set.lesson>Challenging problems on counting elements in subsets of a given finite set</A> 

in this site.