The current price of a non dividend paying stock is 40$. Over each of the next two 3 month period it is expected to rise by 5% and fall by 3%. European put option on the stock have a strike price of 41$ and expiration date in 6 months. The risk free rate is 2% per annum with continuous compounding. Use two period binomial tree to get the risk neutral probability that the stock price will go down in each 3 month period and to get the value of European put option?