{"id":111,"date":"2018-12-11T15:52:09","date_gmt":"2018-12-11T15:52:09","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=111"},"modified":"2018-12-11T15:52:09","modified_gmt":"2018-12-11T15:52:09","slug":"cats-and-rats-and-elephants","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2018\/12\/11\/cats-and-rats-and-elephants\/","title":{"rendered":"Cats and rats and elephants"},"content":{"rendered":"

\"Wall<\/a>A few weeks ago I posted “Lions and Tigers and Bears<\/a>“, which poses a Bayesian problem related to the Dirichlet distribution.\u00a0 If you have not read it, you might want to start there.<\/p>\n

Now here’s the follow-up question:<\/p>\n

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.<\/em><\/p>\n

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?<\/em><\/p><\/blockquote>\n

And here’s my solution<\/p>\n