# Standard deviation of a casino's profit

For the following question, I've determined the mean to be \$0.20, but how do I determine the standard deviation? A slot machine at a casino pays out an average of \$0.9, with a standard deviation of \$120. It costs a dollar per play. If a person plays 2 times, what are the mean and standard deviation of the casino's profit? I've calculated the variance to be$\$120^2=\$14400$, and then$(\$14400)(2^2)=57600$ (since the person played twice), taking square root: SD=$\sqrt{57600}=\$240$. But in fact, the SD=$\$169.71$.

Why?

Update: I now realize that each event is independent and that I should add the variances instead of multiply.

$SD = \sqrt{120^{2} + 120^{2}} = \sqrt{28,800} = 169.7056$