Suppose we have a lognormally distributed $55 stock with a 14% continuously compounded expected rate of return, a 4% dividend yield, and a 25% volatility. The continuously compounded interest rate is 2%. Consider a put option written on the stock that expires in one year with a strike price of K = 65. (a) What is the probability that the put option expires in the money? (b) Assume that you have purchased the put option at time 0 at the Black-Scholes price of $12.7695. What is the probability that your profit at option expiration is positive?