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?
Answer by ikleyn(52776) (Show Source):
You can put this solution on YOUR website! .
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?
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Solution
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 ∩ L) - n(M ∩ U) - n(L ∩ U) + n(M ∩ L ∩ 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. ANSWER
Solved.
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In order for to see many other similar solved problems with detailed explanations, look into the lessons
- Counting elements in sub-sets of a given finite set
- Advanced problems on counting elements in sub-sets of a given finite set
- Challenging problems on counting elements in subsets of a given finite set
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Look also into the links
https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1149313.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1132870.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html
https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1126097.html
https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html
to similar solved problems in the archive of this forum.
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