I think Mr. F slipped at the point noted above; it is

**not** true that if X and Y are i.i.d. random variables then Pr(X + Y < z) = Pr(2 X < z).

Here is an alternative approach which requires some knowledge of the Gamma distribution; see

Gamma distribution - Wikipedia, the free encyclopedia, for example.

If $\displaystyle X_1, X_2, \dots , X_{10}$ are independent random variables with a Gamma distribution and parameters $\displaystyle \alpha \text{ and } \theta$, then their sum has a Gamma distribution with parameters $\displaystyle 10 \alpha \text{ and } \theta$. So the total time to sell 10 tickets has a Gamma distribution with $\displaystyle \alpha = 10 \cdot 3 = 30 \text{ and } \theta = 2$. Hence the probability of being sold out in 60 minutes is $\displaystyle Pr(Y < 60)$ where Y has the Gamma distribution just described. You can find this probability from a table of math functions or you can use something electronic. I used an Excel spreadsheet function, GAMMADIST, to find the probability is about 0.5243.