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ECN437Probability and Expected Value

ECN437Probability and Expected Value - Expected Value The...

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ECN437 Probability and Expected Value Independent Events If two random events are independent of one another, the probability that  both will occur is the product of the probabilities of the individual events. For example, if I flip a coin, the probability that it will land heads up is 0.50  (50%). If I roll a six sided die (the usual kind found in board games), the  chance that it will stop with a 6 on top is 1/6 or about 0.17 (17%). If I do  both at the same time, the chance that the coin will be heads up AND the  die will stop with 6 up are 0.5 * 0.17 = .085 (8.5%). By extension, the  chance that something  else  will happen is 1-0.085 or 0.915 (91.5%).
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Unformatted text preview: Expected Value The expected value of an uncertain event is the sum of the possible payoffs multiplied by each payoff's chance of occurring.Suppose I offer you the following gamble: I roll a six sided die and give you $6 if a 6 comes up, $2 if a 3, 4 or 5 comes up, and nothing otherwise. Since there is a 1/6 chance of each number coming up, the outcomes, probabilities and payoffs look like this: Outco me Probabili ty Pay off 1 1/6 $0 2 1/6 $0 3 1/6 $2 4 1/6 $2 5 1/6 $2 6 1/6 $6 The expected value is sum of the entries in the last two columns multiplied together: (1/6)*0 + (1/6)*0 + (1/6)*2 + (1/6)*2 + (1/6)*2 + (1/6)*6 = $2....
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