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


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

The variance is given by E(X^2) - E^2(X) = [(400^2 \times 0.1) + (0^2 \times 0.1) + (-100^2 \times 0.4)] - [(400\times 0.1) + (0 \times 0.5) + (-100\times 0.4)]^2