1. Consider a deck of four cards, labeled 1?, 1Ο, 2?, and 2Ο. Draw a card, put it back, shuffle the deck, and draw a second card. Compute the expected value of Z = X +Y, where X is the numerical value of the first card and Y is the numerical value of the second card.
2. Above your mirror in the dressing room is a bank of four light bulbs. Each light bulb has a probability of .02 of being out when you flip the switch in your dressing room, and the working ness of each light bulb is independent of the others. Describe the state space of the bank of light bulbs and list the probability of each state.