Answer to Question #28429 in Statistics and Probability for Kathy

Question

I buy an egg to hatch it. The egg can contain a platypus, penguin, or dodo. I can buy as many eggs as I want, but ultimately, I have to get all three animals. Once I have all 3, I will stop buying the eggs. Now, let's say I have hatched a bunch, but have only gotten platypuses and penguins.
Is there a way to determine how many more eggs I will need to hatch to get the dodo?
If the makers of the eggs are using a 3-sided die to determine which animal I will get in the egg, then with each egg, I presumably have a 1-in-3 chance of getting the dodo. Do the odds change if they instead use a 99-sided die (where 1-33=platypus; 34-66=penguin; 67-100=dodo)?