.
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, this probability is the sum 18% + 21% = 39%. ANSWER
It is a DIRECT CONSEQUENCE that the given categories
a) cover the entire universal set, and that
b) the categories are disjoint, i.e. have empty intersections.
It is fully consistent with the general formula of the Elementary probability theory
P(A U B) = P(A) + P(B)
for the disjoint events.
My solution is completed at this point.
----------------
A good style educational / (teaching) tradition assumes and requires that used teaching tools should not
be more complicated than the problem itself.
Or, in other words, the solution should be AS SIMPLE AS POSSIBLE // still remaining to be correct.