6. You take a wrong turn on the way to MIT and end up in Transylvania, where $99 \%$ of the inhabitants are vampires and the rest are regular humans. For obvious reasons, you want to be able to figure out who's who. On average, nine-tenths of the vampires are correctly identified as vampires and nine-tenths of humans are correct identified as humans. What is the probability that someone identified as a human is actually a human?
Solution: Consider a sample of 1000 inhabitants. On average, 990 are vampires and 10 are people. 99 vampires are identified as human and 9 humans are identified as human. So out of the 108 who pass, only $\frac{1}{12}$ are human.