(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 suffer 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 suffer from all three restrictions.
Start with the affliction for all three, which is 17. This goes in the center of the diagram. Next, We have 29 who can't abide garlic and must sleep in their own coffins. We already have 17 that can't abide garlic and must sleep in their own coffins, so we add 12 to the space that is only overlapped by garlic and coffins. Then, we have 36 of holy symbol and coffins. Again, we already have 17 from the first step, so we add 19 to the space only overlapped by holy symbols and coffins. Next, we have 38 for holy symbols and garlic. We put 21 in the space that is only overlapped by holy symbols and garlic. Now 51 for coffins, we add all the numbers that are in the coffin circle, which is 48, so we only enter 3 in the circle only for coffins. We do this for the other two. For a) add up all the numbers and we get 100. So subtract 100 from 120 and we get 20 vampires with no restrictions. For question b) we look at how many total vampires who can't abide garlic. This is 64. Out of these 64, only 14 are garlic alone. So we take 50 (vampires who can't abide garlic plus something else) divided by 64 (total vampires that can't abide garlic, and garlic and something else) and get 78.125%. So the answer to b) is 78.125%.
Apr 11th, 2015
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