Consider two weighted coins. Coin 1 has a probability of 0.3 of turning up heads, and coin 2 has a probability of 0.6 of turning up heads. A coin is tossed once; the probability that coin 1 is tossed is 0.6, and the probability that coin 2 is tossed is 0.4.

The decision maker uses Bayes’ decision rule to decide which coin is tossed. The payoff table is as follows:

(a) What is the optimal action before the coin is tossed?

(b) What is the optimal action after the coin is tossed if the outcome is heads? If it is tails?