Let's say that you have $10000 and you are considering purchasing 2 investments, Apple and Netflix. In one year, Apple can be sold at $X per $1 invested, and Netflix can be sold for $Y per $1 invested. You assume X and Y to be statistically independent random variables. X and Y are normally distributed with a mean of 1.2 and a standard deviation of 0.2.

(i) Let's say you put all your money in Apple, what's the probability that you will be able to sell it one year from now at a positive profit?

(ii) If you split your money evenly between the two investments, what's the probability you will be able to sell your portfolio a year from now for a positive profit?