Mathematically, the expected payback is $9.5.
Below, this is further discussed.
What is the anticipated return?
In general, the likelihood times the value are multiplied together to calculate the projected payback.
E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....
We have two different repayment alternatives in this situation.
Winning
The payback is $500 - $10 = $490
x_1 = 490
The likelihood of winning is one in a thousand (since the choices are 0 to 999)
p(x 1) = 1/1000
Losing
Due to the fact that the person did not win anything, they actually lost $8.
x _2 = -10
The other 999 numbers are regarded as losing numbers because there is only one number that can win.
p(x 2) = 999/1000
E(x) = p(x 1)*x 1 + p(x 2)*x 2 = (1/1000)* 490+ is the expected payback as a result.
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