(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.
Take the sum 71 + 64 + 51 = 186. This could have been the number of vampires that have at least one restriction but those with two restrictions are counted twice and those with all three restrictions are counted thrice.
So we need to make the necessary corrections: 71 + 64 + 51 - 38 - 36 - 29 + 17 = 100 is the number of vampires that have at least one restriction. Finally, 120 - 100 = 20 vampires have none of the three restrictions.