(a) Calculate the expected values of the following lotteries:

(i) 100 with probability 0.4 and 200 with probability 0.5

(ii) 100 with probability p and 200 with probability 1 − p (evaluate the amount as p varies between 0 and 1: does this make sense?); 

(iii) 100 with probability p and if this does not happen (which is the case with probability 1 − p), then another lottery where you get 50 with probability q and 200 with probability 1 − q;

(iv) 100 with probability p, 200 with probability q, 300 with probability r, and nothing with probability 1 − p − q − r.

(b) Suppose that you are asked to participate in a lottery where you get 1,000 with probability 0.1 and 200 otherwise. If you are risk-neutral, what is the maximum you would pay to enter the lottery? Would you be willing to pay more if you were risk-averse? Now suppose that the probability of winning is unknown. If you are risk-averse and willing to pay 600 to enter the lottery, what must be the minimum probability of winning 1,000?