A binary option pays \100$if a stock price exceeds the strike price of$$50$at expiration, and$$0$otherwise. An analyst models the probability that the stock exceeds the strike price as$p(S) = \frac{1}{1 + e^{-(S - 50)/5}}$, where$S$is the current stock price. If the current stock price is$$55$, what is the expected value of the option?