Question

Henry hoards a hundred hens. Every day, each hen lays an egg with probability 0.8 independently of all others. Henry sells each egg for 3 cents, except that on half the days, his dog Barkie breaks half the eggs laid that day (and 1.5 eggs is as sellable as 1), and on the remaining half of the days, Barkie breaks 30 eggs. What is the probability that Henry makes more than a $1.30 today? Instead of summing many probabilities use a well-known approximation and the fact that the sum of independent Gaussians is independent.

Answer 1