The lottery payoff in a letter game at a church social is determined by the single letter the winner holds. There are four letters, A, B, C, and D. The probabilities that each will be drawn are 1/2, 2/10, 4/10 and 3/10 respectively. The payoffs are $2 for an A, $4 for a B, $8 for a C, and $10 for a D. Compute the expected value of the game.
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