Question 1162300
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Formally, the expected value is the sum of each outcome multiplied by its probability.  So in this example the expected value is<br>
{{{(1/5000)*(3496)+(1/5000)*(496)+(4998/5000)*(-4) = (3496+496-19992)/5000 = (-16000)/5000 = -3.2}}}<br>
The expected value is -$3.20.<br>
While that is the formal mathematical way to calculate expected value, in many simple expected value problems like this, there is a much easier way to find the expected value.<br>
In this example, the total cost of the tickets is $20,000; the total payout is $3500+$500 = $4000.  The expected value is then {{{(4000-20000)/5000 = -16000/5000 = -3.2}}}<br>