Problem 6. Miss Ang buys a dozen of eggs (12 eggs in an egg tray) from HS Farm every day, starting at Day 1. For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled.
(a) Find the probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg. Write your answer (applying to (b) and (c) as well) up to 3 decimal point.
(b) Let N be the first day (counted from Day 1) that Miss Ang bought a tray of eggs containing at least one spoiled. Find the expected value of N.
(c) Suppose Day 1 is Sunday. Compute the probability that Day N is also Sunday.
