8 Joe owns a coin that is either a fair coin or a two-headed coin. Imelda believes that there is a 1 2

 chance that the coin is two-headed. She must guess what kind of coin Joe has. If she guesses correctly, she pays Joe nothing, but if she guesses incorrectly, she must pay Joe $2. Before guessing, she may pay 30¢ to see the result of a single coin toss (heads or tails). Determine how Imelda should minimize her expected loss. Also determine EVSI and EVPI.