Please consider the following hypothetical scenario:

Unfortunately, Lana was in a serious automobile accident that has left her with impaired mobility, large medical expenses, and a reduced income. She has filed a personal injury lawsuit against the shipping company whose truck forced her off the road. The company has offered her a one-time cash payment of $300,000 to settle out of court, but her lawyer thinks that she should go to trial instead. On the basis of her lawyers judgments (and a second opinion from a co-workers wife who is an attorney), Lana estimates that she has a 70% chance to win at trial.

Lanas lawyer has a policy that says, You dont owe us a penny unless we get money for you. So if she loses, she wont get any money from the shipping company, but she wont owe any money either. If she wins, the award may be more or less than the $300,000 settlement offer. On the basis of his experience with similar cases, her lawyer simplifies the seemingly infinite set of possibilities. If Lana wins, he figures that theres a 40% chance of her getting a small payoff of $200,000, and a 60% chance of her getting a large payoff of $500,000. These payoffs are net amounts that already reflect the lawyers substantial fees, so they are the amounts that Lana would actually get.

According to expected value theory, what should Lana decide to do? Please show all relevant calculations (by typing out your calculations) and justify your answer based on expected value theory.