a) A factory makes widgets that have a 10% chance of being broken. It ships the widgets to stores in boxes of 4 widgets. If Simon the shopkeeper opens a box of widgets: (I) Find the probability that he will find all widgets broken. (ii) Find the probability that he will find at least one working widget. (iii) Find the probability that he will find all widgets working. b) Suppose that Simon the shopkeeper receives the widgets in a pallet containing 100 boxes. How many widgets in that pallet would you expect to be broken? c) Matthew the magician has a biased coin which when flipped, shows heads 2/3 of the times. If Matt flips his coin twice, what is P? If Matt flips his coin twice, the probability that exact one head will show up is given by? (where X and Y). Matt would have flip his coin N times to ensure that the chance of at least one head showing is greater than 99%? Find P, X, Y, N