It is rumoured that, every year, the Alaskan Easter Bunny brings all children in his state an easter egg filled with 30 chocolates. The eggs are usually filled with 22 milk chocolates and 8 white chocolates, but this year the Mr. Easter has hired some new bunny ladies in the chocolate kitchen, and so this year there are three different types of egg:

Charlie Chocoholic wakes up when Mr. Easter arrives, so he tries to make Charlie fall asleep by telling him about the bunny ladies and their newtypes of egg. But then Charlie just has to check what kind of egg he just got.
Mr. Easter tells him he is allowed 5 chocolates, but no more; the rest must wait until daybreak.

(a) What are your prior probabilities for the three egg types?

(b) Charlie picks 5 chocolates and eats: milk, milk, white, white, and milk.
What are the likelihoods for the 3 egg types?

(c) What are your updated, posterior probabilities for the three egg types?

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10 000 eggs are like the classical ones described above; 4000 eggs have milk chocolate only; 6000 eggs have 15 of each kind.