An option to buy a stock is priced at $$$$300.$ If the stock closes above $30$ on May$15,$ the option will be worth $$$$500.$ If it closes below$20,$ the option will be worth$$ nothing, and if it closes between $20$ and $30($inclusively$),$ the option will be worth $$$$300.$ A trader thinks there is a $40\%$ chance that the stock will close in the$20-30$ range, a $50\%$ chance that it will close above$30,$ and a $10\%$ chance that it will fall below $20$ on May $15.$ How much does she expect to gain?