I have a question which I can't seem to get the answer.

Question:
A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100.

Probability Payoff Net Profit
0.10 500 400
0.50 100 0
0.40 0 -100

Calculate the variance of this rate of return?

Answer given was 20000(% squared).

This is more statistics/math related so I moved your post over here.

For this, I believe you have to do a probability table, for these are discreet variables.

Let X be the amount of profit

Code:

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X      400  0  -100
P(X=x) 0.1  0.5  0.4

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The variance is given by