Question

A survey of 1,007 tourists visiting Orlando was taken. Of those surveyed:
• 266 tourists had visited the Magic Kingdom
282 tourists had visited LEGOLAND
• 50 tourists had visited both the Magic Kingdom and LEGOLAND
59 tourists had visited both the Magic Kingdom and Universal Studios
.89 tourists had visited both LEGOLAND and Universal Studios
• 17 tourists had visited all three theme parks
99 tourists did not visit any of these theme parks
How many tourists only visited the Universal Studios (of these three)?

Answer 1

The number of tourists that only visited the Universal Studios is: 367.

Number of tourists that only visited the Universal Studios

Universal set W of 1007 tourists

Subsets

M of 266 tourists;

L of 282 tourists;

Their in-pairs intersections

ML of 50 tourists;

MU of 59 tourists

LU of 89 tourists

Their triple intersection

MLU of 17 tourists.

Number of tourists who visited only Universal studio

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)

n(M U L U U)= 266 + 282 - 50 - 59 - 89+ 17

n(M U L U U)= 367

Therefore the number of tourists that only visited the Universal Studios is: 367.

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