Consider the two-period binomial tree model for stock price S with S0=4, u=2, d=1/2, N=2. The risk-free interest rate is r=0.3 so that $1 invested today grows to $(1+r) at the end of first period and to $(1+r)^2 at the end of second period. Find the risk-neutral probabilities q and 1-q of S going up and down, respectively. Compute the no-arbitrage price of put option with the strike price K=3 and expiry date T=2. Find the number of shares at t=0 according to the replicating strategy for the put option above.