There is a raffle coming up.
4000 tickets have been sold, and there are 10 prizes to win. I have bought 8 tickets. What are the odds I will win a prize?
Note: each person can only win once. There is no limit as to how many tickets one person can buy. So out of the 4000 tickets, one person can own 1000 tickets. Another person can own just 1 ticket.
Is there a way to calculate my probability of winning or odds of winning?
On
I started writing this as a comment but it became too long, so I'll post it as an answer.
Henry poses an important point with his example in the comments; you cannot determine your probability of winning unless and until you know the distribution of people buying the other tickets.
If I buy the remaining $3992$ tickets, you're guaranteed to win (how nice of me!). And if the remaining $3992$ tickets are bought by $3992$ separate people, the worst-case scenario, your chance of winning can be calculated as:
$$Pr = 1 - \frac{3992 \choose 10}{4000 \choose 10} = 0.0198$$
Explanation: the ten winners are chosen as $4000 \choose 10$. For you to necessarily not be a winner, these winners must be chosen from the remaining contestants, $3992 \choose 10$. Negating this gives the probability at least one of your tickets is in the ten chosen.
Since the probability varies between $2.0$% and $100$%, there definitely isn't a clear way to generalize the solution for all cases.
The probability of you winning a prize depends on the number of people attending the raffle and the number of tickets they bought and who wins the other prizes. For example, if the number of people is less than 10 (including yourself), then you are sure to win. Since the event that you win a prize is not an independent events, we cannot generate a general solution to this problem.