54 people were polled about their vacationing habits.
25 vacationed in western Canada, 31 vacationed in central Canada, 28 vacationed in eastern Canada, 11 vacationed in eastern and western Canada, 10 vacationed in eastern and central Canada, 17 vacationed in western and central Canada, and 4 vacationed in all three regions.
How many people vacationed in at least one of these regions? How many did not?
The question seems really easy to me, but I'm wrong. The answer is 50 and 4, but logically it makes sense to me that everyone vacationed somewhere in one of these places, so all 54 people vacationed somewhere in eastern, central, or western Canada while 0 people didn't vacation at all.
Why am I wrong?
The problem never said all 54 people went on a vacation. The following venn diagram can be used
We know that 4 people went to all 3 places. We also know that 17 people went to Central Canada and West Canada. It then follows that 13 people went only to Central and West Canada. This is because 13 + 4 = 17, adding works because the sets have no intersection(you cant go only to Central and Western Canada and also go to Eastern Canada). This same logic is used to tabulate the results of the venn diagram. You can see that when you add up all the numbers, you get 50. This means that 4 people did not go on vacation.