A stock is currently selling for $50. The stock price could go up by 5% or fall by 5% each month. The monthly risk-free interest rate is 1%. We want to calculate the price of a put option on the stock with an exercise price of $50 and a maturity of two months by using the two-stage binomial method. To that end (a.) Calculate the risk neutral probability that the stock will go up. [if, and only if you cannot find the probability in (a.), use 0.5 for the next two parts) (b.) Find the price of the option mentioned above if it is European (c.) Find the price if it is an American option