Question 1142813
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The solution by tutor @ikleyn shows the standard method for finding expected value, based on the definition.<br>
For this particular problem (and many similar ones), the expected value can be found much more easily.<br>
(1) The total ticket sales are 700($4) = $2800.
(2) The total payouts are $1000 + $500 + 5($100) = $2000.<br>
The total gain by the ticket buyers is $2000-$2800 = -$800; the expected value of each one of the 700 tickets is -$800/700 = -$8/7.