(10 points) A stock price is currently at $50. Assume that at the end of one month the price will be either $60 or $40 (and nothing else!). The risk-free interest rate is 5% per annum with continuous compounding. (a) Compute today's arbitrage-free price of a 1-month European put option written on the stock with a strike price of $50. (b) Carefully explain the arbitrage opportunity which arises if the price of the put option considered in (a) was $6. Provide all necessary details of the strategy and the arbitrage gain