A stock price follows geometric Brownian motion with an expected return () of 15% and a volatility () of 30%. The current price is $45. (Tip: make use of the ln(ST) distribution)

(a) What is the probability that a European call option on the stock with an exercise price of $50 and a maturity date in six months will be exercised?

(b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?