Bob plays a game in which a dice is rolled until an odd number occurs. Bob wins 10 – x dollars if x rolls are needed for x = 1,2 but loses k = 10 dollars if x > 2. Calculate the probability that Bob loses money in this game. Calculate the expected value Bob’s winnings. Calculate the variance of Bob’s winnings. What should be the value of k for the game to be fair, i.e. for the expected value of the money earned to be equal to 0?

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