Question 1165302
.
A survey of 1,119 tourists visiting Orlando was taken. Of those surveyed:
274 tourists had visited the Magic Kingdom
276 tourists had visited LEGOLAND
300 tourists had visited Universal Studios
94 tourists had visited both the Magic Kingdom and LEGOLAND
79 tourists had visited both the Magic Kingdom and Universal Studios
96 tourists had visited both LEGOLAND and Universal Studios
26 tourists had visited all three theme parks
How many tourists had not visited any of these three theme parks?
~~~~~~~~~~~~~~~



<U>Solution</U>


<pre>
We have an universal set W of 1119 tourists

    and its subsets


M of 274 tourists;

L of 276 tourists;

U of 300 tourists;


   their in-pairs intersections

ML of 94 tourists;

MU of 79 tourists

LU of 96 tourists


    and finally their triple intersection

MLU of 26 tourists.


Based on this info, we can easily find the number of tourists who visited at least one of the three parks

    n(M U L U U) = m(M) + n(L) + n(U) - n(M &#8745; L) - n(M &#8745; U) - n(L &#8745; U) + n(M &#8745; L &#8745; U) = 

                   274 + 276 + 300 - 94 - 79 - 96 + 26 = 607.


Then the number of surveyed tourists who had not visited any of these three theme parks is the COMPLEMENT

                   1119 - 607 = 512.     <U>ANSWER</U>
</pre>

Solved.


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