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"Is this reasoning correct" No. The reason why this reasoning is incorrect is that the expected value here depends on the probabilities that envelope 2 contains $2x$ or $x/2$. You have assumed that this is 50/50, but this cannot possibly be the case for all $x$. To see this, suppose that you open envelope 1 and find \$10. You assume that envelope ...


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You have the right idea, make a 4 by 3 payoff matrix with fruit at the top and at the side weather/water yes/no, giving 12 different cells, then put the respective dollar payoffs. You could also make another table and find the expected payoff by multiplying each payoff by its probability, although since all the probabilities are the same, the table wouldn’t ...


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Decision under uncertainty is sometimes called a "game against chance", and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states would form a set of pure strategies for Nature, and Nature commits to a publicly known mixed strategy that randomizes over those pure strategies (assume Nature is ...


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