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On the tapas menu in a local Spanish restaurant customers can order a dish of 20 roasted chillies for £5. There is always a mixture of hot chillies and mild chillies on the dish and these cannot be distinguished except by taste. The restaurant produces two types of dish: one containing 4 hot and 16 mild chillies and one containing 8 hot and 12 mild chillies. When the dish is served, the waiter allows the customer to taste one chilli and then offers a 50% discount to customers who correctly guess whether the dish contains 4 hot chillies or 8 hot chillies. A hungry actuary who regularly visits the restaurant is trying to work out the best strategy for guessing the number of hot chillies.
List the four possible decision functions the actuary could use.
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