Question 1: [17 marks total] (+ 2 bonus) A lottery bond is a type of government bond in which investors receive reduced interest, or none at all, and instead receive a chance of a prize. Examples included the premium bond in the UK. Suppose that the government runs a lottery experiment in order to help them understand how to price the bonds. Suppose they offer small lotteries to consumers that are based on the outcome of a game in which the color red and black appear at random. Let R be the amount of money that the consumer receives if red occurs (the "red state of the world") and B be the amount of money the consumer receives if black occurs (the "black state of the world"). Suppose p is the probability of red, with 0