What Is the Expected Value of a $100 Bet on a Flip

question 14

Essay

What is the expected value of a $100 bet on a flip of a fair coin, where heads pays double and tails pays zero?
E.V.= 0.5($200) + 0.5($0) = $100
E.V.= PH (H) + PT(T); where H is the payoff from the coin turning up heads and T is the payoff if the coin turns up tails.PH and PT are the probabilities of the coin turning up heads or tails respectively.Substituting actual values in out formula reveals:

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