I have a probability of $\frac{24}{800000}$ to win with one lottery ticket. What if I buy two tickets? Assuming there's a lottery with 800,000 tickets and 24 of these tickets contain a win, my chance to win (if I buy only one ticket) is $\frac{24}{800,000}$ or $\frac{1}{33,333.\overline{3}}$, right?  
But what are my chances to win if I buy two tickets?

Your chances to win at least once are roughly twice as high if you buy two tickets.  Not exactly twice, because there is a very small chance both tickets will win, but this is small enough to ignore in an approximation.
