Suppose that there is a coin with an unknown probability of a heads. i. What would the principle of insufficient reason assign as the prior on the coin? ii. Suppose the coin produces a random variable such that a heads wins $110 and a tails loses $100. Would a risk neutral gambler be willing to make this bet if the density characterizing the probability of heads is not known? (For this question risk neutral means expected profit maximizer which is equivalent to the expected loss minimizer.) iii. Suppose that the risk neutral gambler were informed that the true probability of the coin is .5. Would this gambler assess the bet differently than if they employed principle of insufficient reason? iv. Suppose that the coin probability is known to be drawn from a uniform (0,1) density. How would a gambler with Hurwicz preferences assess the bet differently from a risk neutral gambler if the bet is to be taken prior to the draw of the coin probability? v. Suppose that the probability density of heads will, with probability be drawn from the uniform density on (0, .5) and probability on (.5, 1). Would an expected profit maximizer behave any differently than if they were told the coin is uniform on (0,1)