The price of a European call that expires in six months and has a strike price of $49 is $4.5. The underlying stock price is $50, and a dividend of $1.00 is expected in three months. The term structure is flat, with all risk-free interest rates being 10%.

a. What is the price of a European put option that expires in six months and has a strike price of $49? [1 mark]

b. Explain in detail the arbitrage opportunities if the European put price is $1.60. How much will be the arbitrage profit? [4 marks]