A few weeks ago I posted “Lions and Tigers and Bears“, which poses a Bayesian problem related to the Dirichlet distribution.  If you have not read it, you might want to start there.

Now here’s the follow-up question:

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?

And here’s my solution