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

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State of Nature Alternative Coin 1 Tossed Coin 2 Tossed Say coin 1 tossed Say coin 2 tossed 0 0 Prior probability 0.6 0.4