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(a) Calculate the expected values of the following lotteries: (i) 100 with probability 0.4 and 200 with probability 0.5 ; (ii) 100 with probability p and 200 with probability 1-p (evaluate the amount as p varies between 0 and 1 : does this make sense?); (iii) 100 with probability p and if this does not happen (which is the case with probability 1-p ), then another lottery where you get 50 with probability q and 200 with probability 1-q ; (iv) 100 with probability p, 200 with probability q, 300 w
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