The logarithmic return for a stock is normal with an annualized mean of 12% and an annualized standard deviation of 50%.

1. [5pts] Assume you were thinking of buying the stock. What is the probability that in six months time you will lose money? Show each step of your calculation.
2. 5pts] If the analysis took place in a risk neutral economy, what would be the estimated probability of losing money? Show each step of your calculation.