Suppose 120 vampires are at an undead convention. They have the following
Mathematics

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(a) How many vampires have none of the three restrictions?
(b) If we select a vampire at random from among those who can't abide garlic, what is the probability that
they suff er from another restriction as well?
71 shy away from holy symbols; 64 can't abide garlic;51 must sleep in their own coffins; 38 shy away from h.s. and can't abide garlic;36 shy away from h.s. and must sleep in their own coffs; 29 can't abide garlic and must sleep in their own coffs;17 suff er from all three restrictions.
What makes this problem harder is that when they say that 64 don't like garlic, that 64 also includes the ones that suffer from other restrictions. To solve the problem, we have to isolate the vampires that are only in one group or another. We start at the center, the ones that suffer from all three.
Annotation is as follows:
Shy from h.s.=H
Dislikes Garlic=G
Sleeps in Coffin=C
O' comes before the groups that are not anything besides
So we find O'HC, those that shy away from h.s. and sleep in their coffin, but do not fear garlic.
O'HC=3617=19
Repeating that with the others:
O'HG=3817=21
O'GC=2917=12
Now we find O'H, O'G, and O'C, which we do the same thing except we subtract all other groups that include that letter.
O'H=71172119=14
O'G=64172112=14
O'C=51171219=3
So now that we've isolated each group, including that 17 group which you can call O'HGC, we subtract all those numbers from the 120 total number of vampires to find how many do not suffer any restrictions.
So:
1201421171419123=20
20 is the answer for (a)
For (b), we add up all those that suffer from something else in the G group, then divide by the total of 64 to give us the probability.
12+17+21=50
50/64=78.125% is the answer
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