Consider a game where there are three possible earning amounts, ranging from 1 to 3. The probability of winning an amount N is given by 1 KN , where K is a fixed value and N takes values from 1 to 3. (a) Calculate K (b) Determine the expected earning for each game.
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A carnival game consists of three dice in a cage. A player can bet a dollar on any of the numbers 1 through 6. The cage is shaken, and the payoff is as follows. If the player's number doesnt appear on any of the dice, he loses his dollar. Otherwise, if his number appears on exactly k of the three dice, for k = 1; 2; 3, he keeps his dollar and wins 2k more dollars. What is his expected gain from playing the carnival game once?
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