Here’s another Bayes puzzle:
Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don’t know how many of each there are.
During the tour, we see 3 lions, 2 tigers, and one bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species.
What is the probability that the next animal we see is a bear?
Will Koehrsen posted an excellent solution here. His solution is more general than mine, allowing for uncertainty about the parameters of the Dirichlet prior.
Cats and rats and elephants
Now that we solved the appetizer, we are ready for the main course…
Suppose there are six species that might be in a zoo: lions and tigers and bears, and cats and rats and elephants. Every zoo has a subset of these species, and every subset is equally likely.
One day we visit a zoo and see 3 lions, 2 tigers, and one bear. Assuming that every animal in the zoo has an equal chance to be seen, what is the probability that the next animal we see is an elephant?