A stock price follows geometric Brownian motion with an annual expected return of 6% and a volatility of 35%. The current price is $38.
a) What is the probability that a European call option on the stock with an exercise price of $40 and a maturity date in 12 months will be exercised?
b) What is the probability that the holder of the European call option on the stock will profit $4.5 upon exercising the option?