Step-by-step explanation:
you understand how a venn diagram works ?
you have to put elements or the amount of elements into the different segments. there are segments that belong to only one category, segments with elements that are shared between 2 neighboring categories, and in this case 1 segment in the middle that has all elements shared between all 3 categories.
so, we know, the total of all elements (fans) is 36.
now imagine we place every fan exactly into the segment, where his or her allegiance lies.
the easiest way to start is with the center. there are 5 fans there, so write 5 in there.
these 5 people are therefore also part of the total number of Wild fans, of the Viking fans and the Twins fans, and of all the shared segments, of course.
so, we have only 7-5 = 2 shared Wild and Vikings only fans (in the segment above the center segment). they are not fans of the Twins.
we have 9-5 = 4 shared Wild and Twins only fans (in the segment left below the center). they are not fans of the Vikings.
we have 11-5 = 6 shared Vikings and Twins only fans (in the segment right below the center). they are not Wild fans.
what is left for the pure, single team fans ?
the Wild have 12-5-2-4 = 1 pure fan.
the Vikings have 16-5-2-6 = 3 pure fans.
the Twins have 22-5-4-6 = 7 pure fans.
so, we have 1+3+7 = 11 pure fans, 2+4+6 = 12 double team fans, and 5 all 3 teams fans. but that is only 28 fans altogether.
so, something is not right with the data here.
I assume we have 28 total from now on.
for Viking AND Wild fans we have the 2 fans that only like these 2 teams plus the 5 that like all 3 teams (including the Vikings and the Wild) = 7 out of the total of 28 fans.
the probability to pick one of them is then
7/28 = 1/4 =0.25
if the total of 36 questioned fans is still there and explained maybe outside of the given venn diagram (e.g. were asked but are fans of a totally different team or of no team at all), then the probability would be
7/36 = 0.194444444...
