Solve the problem.
-In a survey of 189 vacationers in a popular beach resort town, 73 indicated they would consider buying a home there, 73 would consider buying a beach villa, 59 would consider buying a lot, 24 would consider both a home
And a villa, 27 would consider both a home and a lot, 26 would consider both a villa and a lot, and 12 would
Consider all three. How many vacationers would not consider any of the three? How many would consider only
A home?
A) 49; 18
B) 49; 35
C) 61; 46
D) 49; 34

Question

Quizplus · Accepted Answer

To solve this problem, we use the principle of inclusion-exclusion to avoid double-counting those who are interested in more than one option. The total number of vacationers interested in at least one option is calculated as follows:- Total interested in a home, a villa, or a lot = 73 (home) + 73 (villa) + 59 (lot)- Subtract those interested in both options to avoid double counting = -24 (home and villa) - 27 (home and lot) - 26 (villa and lot)- Add back those interested in all three options, as they were subtracted twice in the previous step = +12This gives us: $73 + 73 + 59 - 24 - 27 - 26 + 12 = 140$Therefore, the number of vacationers not interested in any of the three options is the total number of vacationers minus those interested in at least one option: $189 - 140 = 49$.To find how many would consider only a home, we take the total number interested in a home and subtract those interested in a home and at least one other option:- Total interested in a home = 73- Subtract those interested in a home and at least one other option = -24 (home and villa) - 27 (home and lot) + 12 (since those interested in all three were subtracted twice)This gives us: $73 - 24 - 27 + 12 = 34$.Thus, 49 vacationers would not consider any of the three options, and 34 would consider only a home.

Solve the Problem. -In a Survey of 189 Vacationers in a Popular Beach