ABC Corp. currently has a stock price of $70 per share. The stock price could go up to $77 or go down to $59.5 in six months. Annual risk-free rate is equal to 5%. You want to evaluate a European put option (X=$65) on this stock with the maturity of six months.

1. Using the binomial tree method to price the put option. (5 points)
2. Using the put call parity, find the price of a call option with the same maturity and strike price as the put option in part 1. (2 points)

3. If the put option is quoted as $4 in the market right now, show how you can make risk-less profits through arbitrage (9 points)