Mathematical finance question on options

Problem 1. (10 Points) Consider a two-step Binomial model. In Figure 1 you are given an incomplete pricing tree, which correSponds to a EurOpean put Option with strike price X = 65. 0 / 2655 / \\ 1353(0) 14.6 \\ / 17E \\ 35.6 Figure 1: European put with X = 65 of Problem 1. (a) (3 Points) Compute the per period interest rate r and the risk-neutral probability p*. (b) [1 Points) Find the price of the put option at t : 0. (c) [6 Points) Determine the complete binomial tree for the stock price