Question: Suppose one morning you pick two eggs for lunch at random from a dozen eggs in your refrigerator, thinking that they are all hard-boiled. You then learn that in fact four of the eggs have not been hard-boiled,
a) What is the probability that your two lunch eggs are both hard-boiled?
b) Given that you crack one of your lunch eggs and find it is hard-boiled, what is the probability that the second egg is hard boiled?