Assume the Black-Scholes framework for a stock. You are given:

i) The current stock price is 40

ii) The stock pays no dividends

iii) The expected rate of appreciation is 16%

iv) The stocks volatility is 30%

v) The Black-Scholes price of a 6-month 42-strike European call on the stock is 3.22

vi) The continuously compounded risk-free rate is 8%

You just bought a 6-month straddle which pays the absolute difference between the stock price after 6 months and 42.

Calculate the probability of having a positive profit after 6 months.

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A) Less than 0.35

B) At least 0.35 but less than 0.40

C) At least 0.40 but less than 0.45

D) At least 0.45 but less than 0.50

E) At least 0.50