Question 1164115: A survey of 1,062 tourists visiting Orlando was taken. Of those surveyed:
273 tourists had visited the Magic Kingdom
266 tourists had visited LEGOLAND
298 tourists had visited Universal Studios
94 tourists had visited both the Magic Kingdom and LEGOLAND
75 tourists had visited both the Magic Kingdom and Universal Studios
56 tourists had visited both LEGOLAND and Universal Studios
33 tourists had visited all three theme parks
How many tourists had not visited any of these three theme parks?
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Today I just solved a similar (but much more complicated) problem for you under this link
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1164119.html
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1164119.html
Use the formula (1) from that solution
n(A U B U C) = n(A) + n(B) + n(C) - n(AB) - n(AC) - nBC) + n(ABC) (1)
which is valid for any three subsets A, B, C of a universal set, their in-pair intersections AB, AC and BC, and the triple intersection ABC.
Substitute all given data into the formula and obtain
the number of tourists who visited at least one of the three parks = 273 + 266 + 298 - 94 - 75 - 56 + 33 = 645.
The complement to it, 1062 - 645 = 417 is the ANSWER to your question.
Solved.
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I like to get "THANKS" from students for my work and for my teaching.
So, I expect to get your "DEEPEST THANKS" soon.
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