Question

In an amusement park, a visitor gets to ride on three different rides (A, B and C) for free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited the amusement park on that day?

Accepted Answer

E. Since no visitor opted for both B and C, $n(B \cap C) = 0$ and $n(A \cap B \cap C) = 0$. For set A: $n(A \cap B) = 22$, $n(A \cap C) = 25$, so only A = $77 - 22 - 25 = 30$. For set B: $n(A \cap B) = 22$, so only B = $55 - 22 = 33$. For set C: $n(A \cap C) = 25$, so only C = $50 - 25 = 25$. 40 visitors did not opt for A or B, so they are either in C only (25) or none. Thus None = $40 - 25 = 15$. Total visitors = $30 + 33 + 25 + 22 + 25 + 15 = 150$.

Venn Diagram: Amusement Park Rides

Explanation

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