Question 1153206
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<pre>

In my previous post,


    https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1153204.html


I just answered the first question, saying that the answer is the complement of 18% to 100%, i.e.  100% - 18% = 82%.


So, the union of the two sets, athletics and social, is 82% of the entire population.


Each of the components, athletic and social, is 61% and 48%, respectively.


Hence, their intersection is  61% + 48% - 82% = 27%.    <U>ANSWER</U>.
</pre>

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The major fact you need to know to solve such problems is that


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;n(A U B) = n(A) + n(B) - n(A &#8745; B)


for subsets A, B, (A U B) and (A &#8745; B) of a universal set,

where n(X) is the number of elements of subset X.



See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

in this site.