Question 1120592
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The expected value is the sum of all the different payouts, each multiplied by the probability of the corresponding outcome.<br>
One possible outcome is the ball landing on 4; probability 1/38; payout +245.
The other possible outcome is the ball landing on any other number: probability 37/38, payout -7.<br>
The expected value is<br>
{{{(1/38)(245)+(37/38)(-7) = (245-259)/38 = -14/38 = -7/19.}}}<br>
If you played the game 1000 times, the amount you would expect to lose is
{{{1000(7/19) = 7000/19 = 368}}} (rounded to the nearest dollar, since each payout is a whole number of dollars).