Question

You are given the opportunity to guess whether a coin is fair or two-headed, where the prior probabilities are 0.5 for each of these possibilities. if you are correct, you win $5; otherwise, you lose $5. you are also given the option of seeing a demonstration flip of the coin before making your guess. you wish to use bayes' decision rule to maximize expected profit.

Answer 1

the probability may be .....................find ur answer in dots

Answer 2

decision alternatives area1: Guess that the coin is fair,a2: Guess that the coin is two-headed. The states of nature are1: The coin is a fair coin,2: The coin is a two-headed coin.The payoff table is given below.State of NatureDecisionAlternative1Fair Coin22-headed coina1 (guess fair)5-5a2 (guess 2-headed)-5 5Prior probability0.50.5(b)The two decision alternatives tie for being optimal, since both give an expected payoff of $0.