Consider a one-step binomial tree on stock with a current price of $60 that can go either up to $70 or down to $50 in 1 year. The stock does not pay dividend and interest rates are zero. We want to price the 1-year $65-strike European put option on this tree.

(i) What's the put option payoff 1 year later if the stock price ends up at $70? (integer)

(ii) What's the payoff if the stock price ends at $50? (integer)

(iii) Use the tree to compute the value and delta of the put option (two decimals).

(iv) What's the risk-neutral probability of the stock price going up to the $70 mode of the tree ? (two decimals)