Question 1151297
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            Honestly, I don't know and don't understand  WHY  the respectful tutor Jim chose this complicated way to solve the problem.


            It can be solved in  MUCH  SIMPLER  way,  and I will show it to you now.



You have the universal set of all people surveyed.


        Notice that  17% + 18% + 29% + 21% + 15% = 100%,  so these subsets cover the entire set.


Now,  from the text,  it should be clear to you that all listed categories of people are  DISJOINT : 
the intersections between any two different categories are  EMPTY.


        It is clear and obvious from the definitions of these categories in the post.



Now,  the question is :   what is the probability to randomly select from the union of the  {18%}  and  {21%}  subsets.


But of course, &nbsp;this probability is the sum  &nbsp;18% + 21% = 39%.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   <U>ANSWER</U>



It is a &nbsp;<U>DIRECT &nbsp;CONSEQUENCE</U> &nbsp;that the given categories 


<pre>
    a)  cover the entire universal set, &nbsp;&nbsp;&nbsp;&nbsp;and that

    b)  the categories are disjoint, i.e. have empty intersections.
</pre>

It is fully consistent with the general formula of the Elementary probability theory

    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;P(A U B) = P(A) + P(B) 

for the disjoint events.


My solution is &nbsp;<U>completed</U> &nbsp;at this point.



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A good style educational / (teaching) &nbsp;tradition assumes and requires that used teaching tools should not 
be more complicated than the problem itself.


Or, &nbsp;in other words, &nbsp;the solution should be &nbsp;AS &nbsp;SIMPLE &nbsp;AS &nbsp;POSSIBLE &nbsp;&nbsp;// &nbsp;&nbsp;still remaining to be correct.