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Sagot :
Answer:
129 tourists
Step-by-step explanation:
Let 'A' represent the tourists that visited LEGOLAND, let 'B' represent the tourists that visited Universal Studios, and let 'C' represent the tourists that visited Magic kingdom
The total number of tourists, n = 1,076
The number of tourist surveyed that visited only LEGOLAND = A∩B'∩C' = 297 tourist
The number of tourist that visited only Universal studios, B∩A'∩C' = 275 tourist
The number of tourist that visited both the Magic Kingdom and LEGOLAND, A ∩ B' ∩ C = 85 tourist
The number of tourist that visited both the Magic Kingdom and Universal Studios, A' ∩ C ∩ B = 88 tourists
The number of tourist that visited both the LEGOLAND and Universal Studios, A ∩ B ∩ C' = 73 tourist
The number of tourist that visited all three theme parks, A ∩ B ∩ C = 34 tourist
The number of tourists that did not visit any of these theme parks = 95 tourists
In set theory, we have for three sets
A ∪ B ∪ C = A∩B'∩C' + B∩A'∩C' + C∩A'∩C' + A ∩ B' ∩ C + A' ∩ C ∩ B + A ∩ B ∩ C' + A ∩ B ∩ C
A ∪ B ∪ C = 1,076 - 95 = 981
∴ The number of tourists that only visited Magic Kingdom, 'C∩A'∩C' ', is given as follows;
C∩A'∩C' = A ∪ B ∪ C - (A∩B'∩C' + B∩A'∩C' + A ∩ B' ∩ C + A' ∩ C ∩ B + A ∩ B ∩ C' + A ∩ B ∩ C)
∴ C∩A'∩C' = 981 - (297 + 275 + 85 + 88 + 73 + 34) = 129
The number of tourists that only visited the Magic Kingdom, C∩A'∩C' = 129 tourist
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