Probability Questions dealing with risk

[LegendofLink]

this has to do with economics and probability and risk. anyway, the problem is thus.

Would a risk-averse person accept a bet where he wins $550 with 10% probability, $175 with 30% probability and loses $150 with 60% probability? What is the expected payoff of the above bet?

Should I just plot a graph for this and determine what the curve is doing at the relative points to determine this, and also for the second part, isn't the answer just 17.5 since i multiply the win amounts by probability, add them, the subtract the loss amount times it's probability?

next question: What is the expected utility of accepting the above bet if the initial wealth is $1050 and the utility function is U = W^1/2?

can utility be negative, i can calculate the utility for the win amounts, but for the loss would it be 0 or can it be a negative value?

[TomCollins]

First part:
.1*550 + .3*175 + .6*-150 = 17.5

Convert $ to Utility.

Before the bet, U = 32.4

After the bet, he has 10% of being at 40, 30% of being at 35, and 60% of being at 30.

This puts an EV of U at 32.5. This is higher than 32.4, so he'll take it.